Denna text är delvis en dokumentation av min egna resa inom datorbaserat tonsättande, specifikt inom algoritmisk komposition. Det är även ett utforskande av den tankevärld som finns i anknytning till dessa metoder – där estetiska koncept och konsekvenser diskuteras. Texten kommer huvudsakligen att beröra metoder som gynnas av eller möjliggörs av teknologi. Jag har försökt att närma mig dessa ämnen holistiskt genom att diskutera allt från estetik, teknik, till konkreta realiseringar av särskilda musikaliska idéer. Till detta tillkommer även många notexempel, lite kod, och illustrationer – specifikt för att stödja förklaringarna av, för många musikstudenter, främmande utommusikaliska koncept.

Les systèmes d'assainissement urbain sont des objets qui assurent une fonction hydrologique (concentration et évacuation des eaux d'origine météorique) à partir de réseaux de canalisations dont les structures sont en perpétuelle évolution.<br />Après avoir constaté que les modèles représentant l'activité hydrologique des réseaux furent basés sur une approche centrée sur le seul pôle fonctionnel et noté l'insuffisance d'une telle position, il est proposé de recentrer la modélisation de l'objet en reliant le pôle fonctionnel au pôle structurel; liaison entre ce qu'est et ce que fait l'objet. La théorie de la Dimension Fractale, et en particulier l'utilisation du concept de dimension d'homothétie, permettent de concevoir un modèle de structure des réseaux principalement ramifiés. La forme d'un réseau d'agglomération est alors représentée à partir de sa complète décomposition (non unique) en sous systèmes structurés par des réseaux morphologiquement quantifiés par une dimension d'homothétie statistique comprise entre un et deux. La validation expérimentale de ce modèle enrichit son sens initial. En effet, les structures sont évolutives ; leur état est quantifié à partir d'une mesure de l'état de celui-ci relativement à l'objet fractal théorique par le biais d'Un coefficient de complétude. Le modèle étant compatible avec le fait hydrologique, est décrit le mode de formalisation d'un modèle fonctionnel qui conjugue par convolution deux distributions, l'une relative au sol et l'autre au réseau. Le fonctionnel et le structurel sont reliés l'un à l'autre; le modèle est globalement, un modèle morpho-fonctionnel.

This thesis explores new approaches to the analysis of functions by combining tools from the fields of complex bases, number systems, iterated function systems (IFS) and wavelet multiresolution analyses (MRA). The foundation of this work is grounded in the identification of a link between two-dimensional non-separable Haar wavelets and complex bases. The theory of complex bases and this link are generalized to higher dimensional number systems. Tilings generated by number systems are typically fractal in nature. This often yields asymmetry in the wavelet trees of functions during wavelet decomposition. To acknowledge this situation, a class of extensions of functions is developed. These are shown to be consistent with the Mallat algorithm. A formal definition of local IFS on wavelet trees (LIFSW) is constructed for MRA associated with number systems, along with an application to the inverse problem. From these investigations, a series of algorithms emerge, namely the Mallat algorithm using addressing in number systems, an algorithm for extending functions and a method for constructing LIFSW operators in higher dimensions. Applications to image coding are given and ideas for further study are also proposed. Background material is included to assist readers less familiar with the varied topics considered. In addition, an appendix provides a more detailed exposition of the fundamentals of IFS theory.

This thesis investigates the underlying causes of friction and ine ciency within an internal combustion engine, focusing on the ring-liner conjunction in the vicinity of the power-stroke top dead centre reversal. In such lubricated contacts, friction is the result of the interplay between numerous kinetics, with those at micro- and nano-scale interactions being signi cantly di erent than the ones at larger scales. A modi ed Elrod's cavitation algorithm is developed to determine the microscopic tribological characteristics of the piston ring-liner contact. Predicting lubricant tran- sient behaviour is critical when the inlet reversal leads to thin lms and inherent metal-to-metal interaction. The model clearly shows that cavitation at the trailing edge of the ring-liner contact generated pre-reversal, persists after reversal and pro- motes starvation and depletion of the oil lm. Hence, this will lead to boundary friction. A fractal based boundary friction model is developed for lightly loaded asperity con- tacts, separated by diminishing small lms, usually wetted by a layer of molecules adsorbed to the tips of the asperities. In nano-scale conjunctions, a lubricant layering e ect often takes place due to the smoothness of surfaces, which is governed by the surface and lubricant properties. A molecularly thin layer of lubricant molecules can adhere to the asperities, being the last barrier against direct surface contact. As a result, boundary friction (prevailing in such diminishing gaps) is actually determined by a combination of shearing of a thin adsorbed lm, adhesion of approaching as- perities and their plastic deformation. A model for physio-chemical hydrodynamic mechanism is successfully established, describing the formation of thin adsorbed lms between asperities. This model is e ectively integrated with separately devel- oped models that predict the adhesive and plastic contact of asperities.

An understanding of the spatio-temporal dynamics of marine predator populations is essential for the sustainable management of marine resources. Tagging studies are providing ever more information about the movements and migrations of marine predators and much has been learned about where these predators spend their time. However little is known about their underlying motivations, making it difficult to make predictions about how apex predators will respond to changing environments. While much progress has been made in behavioural ecology through the use of optimality models, in the marine environment the necessary costs and benefits are difficult to quantify making this approach less successful than with terrestrial studies. One aspect of foraging behaviour that has proved tractable however is the optimisation of random searches. Work by statistical physicists has shown that a specialised movement, known as Lévy flight, can optimise the rate of new prey patch encounters when new prey patches are beyond sensory range. The resulting Lévy flight foraging (LFF) hypothesis makes testable predictions about marine predator search behaviour that can be addressed with the theoretical and empirical studies that form the basis of this thesis. Results presented here resolve the controversy surrounding the hypothesis, demonstrating the optimality of Lévy searches under a broader set of conditions than previously considered, including whether observed Lévy patterns are innate or emergent. Empirical studies provide robust evidence for the prevalence of Lévy search patterns in the movements of diverse marine pelagic predators such as sharks, tunas and billfish as well as in the foraging patterns of albatrosses, overturning a previous study. Predictions from the LFF hypothesis concerning fast moving prey are confirmed leading to simulation studies of ambush predator’s activity patterns. Movement analysis is then applied to the assessment of by-catch mitigation efforts involving VMS data from long-liners and simulated sharks.

Student Number : 0318623R - PhD thesis - School of Geosciences - Faculty of Science / Physical and chemical properties of atmospheric particles are fundamental but not necessarily easily accessible parameters. Uncertainties in these parameters are responsible for some uncertainties associated with radiative impacts of aerosol particles in global climate models. The uncertainties pertain to limitations of sampling and measurement devices, difficulties in modelling aerosols (source strengths, spatial and temporal variability) and in understanding microphysical and optical properties of aerosol particles. Physical and chemical properties can be obtained at single-particle level by microscopy analyses of individual particles. Using refined analytical and interpretative techniques to derive some of these fundamental properties, aerosol particles collected in various field campaigns and laboratory experiments were investigated using two high resolution microscopes. The particles were collected during the LBA-EUSTACH, Large-Scale Biosphere-Atmosphere Experiment part of European Studies on Trace Gases and Atmospheric Chemistry; SMOCC campaign, Smoke Aerosols, Clouds, Rainfall and Climate; CTBH II, Cape Town Brown Haze II campaign; and a controlled combustion experiment. Microscopy techniques were compared and complemented with conventional techniques to characterise particle sizes, shapes, chemical compositions and mixing states. Particle size distributions were compared between geometric equivalent sizes measured from microscopes and aerodynamic equivalent diameters, while taking into account particle densities. Large differences were found between the particle sizing techniques. Microscopy sizes (3D) were systematically lower than expected, and depended on the relative humidity during particle sampling. Differences were attributed to loss of mass, presumably water adsorbed on particles. Losses were high and could not be accounted for by known humidity growth factors suggesting losses of other volatile compounds adsorbed on particles as well. Findings suggest that there are inherent problems in defining particle sizes with different sizing techniques, despite accounting for humidity growth of particles and particle density. For collected particles, there are mass losses on individual particles, as opposed to particle losses to walls during sampling. These losses will inevitably bias observed mass distributions derived from collected particles and hence their number-size distributions. Relatively young aggregated soot particles from wood combustion were investigated for particle morphology (fractality, specific mass) and dynamic properties. Based on a procedure that has been validated on modelled aggregates, several important parameters to characterise geometry and drag-to-mass relationship of aggregates were derived. Three techniques were used to derive fractal dimension of soot aggregates. Averaged fractal dimension was found to be Df = 1.82 ± 0.08. Dynamic shape factors of soot particles were 1.7 to 2.5 and increasing with mass of aggregates. In the regime 0.2 < Kn < 0.7 (Knudsen number, Kn = 2#21;/dmob) the mobility diameter dmob was observed to be proportional to the radius of gyration with a ratio dmob/2Rg = 0.81 ± 0.07. Specific surface area of aggregates was determined to be 70 ± 10 m2g−1 based on SEM image analysis. These parameters can be used directly in modelling microphysical behaviour of freshly formed soot particles from biomass combustion with fractal dimension of Df ≈ 1.80. Chemical composition and size distributions of particles were investigated on filter samples collected during intense winter brown haze episodes in Cape Town. The sampling technique offered the capability to characterise highly heterogeneous aerosols over a polluted urban environment. Based on morphology and elemental composition, particles were categorised into seven particle groups of: aggregated soot particles, mineral dust, sulphates (SO2− 4 ), sea-salt, tar balls/fly ash, rod-shaped particles associated with soot agglomerates and those that could not be attributed to any of these groups were labelled as ‘others’. Apportionments of chemical species were highly variable both spatially and temporally. These variations indicate lack of lateral mixing and dependence of particle chemical compositions on localised and point sources within the Cape Town area. Sulphate and aggregated soot particles were externally mixed with fractional number concentrations of 0− 82% and 11%−46%, respectively. Aerosol complex refractive indices were derived from the chemical apportionment and particle abundance determined in microscopy analyses. The refractive indices were combined with in-situ measurements of number-size distribution to determine optical properties of aerosols. Single scattering albedo, !0, varied from 0.61 to 0.94 with a mean value of 0.72±0.08. The !0 is much lower than is generally reported in literature, and this was attributed to high concentrations of highly absorbing anthropogenic soot observed in SEM analysis. The mean extinction coefficient #27;ep was 194 ± 195 Mm−1. #27;ep and !0 clearly demonstrated and explained quantitatively the visibility reduction due to particles in the Cape Town atmosphere, reduction observed as the brown haze phenomenon. In all the three case studies, microscopy single particle analysis played a critical role in advancing knowledge of understanding properties of aerosol particles in the atmosphere.

A fractal stochastic point process (FSPP) is used to model molecular evolution in agreement with the relationship between the variance and mean numbers of synonymous and nonsynonymous substitutions in mammals. Like other episodic models such as the doubly stochastic Poisson process, this model accounts for the large variances observed in amino acid substitution rates, but unlike other models, it also accounts for the results of Ohta's (1995) analysis of synonymous and nonsynonymous substitutions in mammalian genes. That analysis yields a power-law increase in the index of dispersion and an inverse power-law decrease in the coefficient of variation with the mean number of substitutions, as predicted by the FSPP model but not by the doubly stochastic Poisson model. This result is compatible with the selection theory of evolution and the nearly-neutral theory of evolution.

The efficient market hypothesis is one of the most important propositions in finance theory and has been subjected to years of rigorous empirical testing. We examine power of a new tool for evaluating market efficiency, fractal dimension. Characteristics and abilities of fractal dimension measure are explored through extensive Monte Carlo simulations. We prove that it provides an accurate evaluation of market's efficiency and its changes. This approach is highly innovative and creates new possibilities for examination of markets. The uniqueness of fractal dimension is in its ability to assign a numerical ranking to examined series describing the level of (in)efficiency; it is accurate for small samples of observations and quickly reflects changes in market efficiency structure. Powered by TCPDF (www.tcpdf.org)

On sait que la matrice d'incidence associée à une substitution ne suffit pas pour déterminer complètement le système dynamique associé, même dans des cas très simples, il existe plusieurs substitutions associées à une même matrice car il existe de nombreux mots ayant le même abélianisé. Dans cette thèse, on étudie les points communs de deux lignes brisées associées à deux substitutions $sigma_1$ et $sigma_2$ irréductibles unimodulaires de type Pisot qui ont la même matrice d'incidence. On identifie les points communs de ces deux lignes brisées à partir d'un algorithme. On montre ainsi que l'intersection de ces deux lignes brisées est aussi une ligne brisée associée au point fixe d'une nouvelle substitution. On montre plus précisément que si $sigma_1$ vérifie la conjecture Pisot et $0$ est un point intérieur à son fractal de Rauzy alors ces points communs peuvent être engendrés par une substitution définie sur un alphabet appelé alphabet des paires équilibrées. Cette substitution est obtenue à partir d'un algorithme, l'algorithme des paires équilibrées. On obtient ainsi l'intersection des intérieurs des deux fractals de Rauzy. En prenant la clôture de cet ensemble on obtient un ensemble substitutif. La condition que $0$ est un point intérieur au fractal de Rauzy associé à la substitution $sigma_1$ nous permet de montrer que l'intersection des deux fractals de Rauzy est de mesure positive. Dans une deuxième partie du travail on s'intéresse à l'étude de la frontière du fractal de Rauzy. Le fractal de Rauzy est dit fractal mais c'est en fait sa frontière qui est fractale. / The matrix of a substitution is not su&#64259;cient to completely determine the dynamics associated with it, even in the simplest cases since there are many words with the same abelianization. In this paper we study the common points of the canonical broken lines associated with two di&#64256;erent irreducible Pisot unimodular substitutions &#963;1 and &#963;2 having the same incidence matrix. We prove that if &#963;1 veri&#64257;es the Pisot conjecture and 0 is an inner point to the Rauzy fractal associated with the substitution &#963;1 then these common points can be generated with a substitution on an alphabet of so-called balanced pairs, and we obtain in this way the intersection of the interior of two Rauzy fractals.

Techniques for procedural generation of the graphics content have seen widespread use in multimedia over the past thirty years. It is still an active area of research with many applications in 3D modeling software, video games, and films. This thesis focuses on algorithmic generation of virtual terrains in real-time and their real-time visualization. We provide an overview of available approaches and present an extendable library for procedural terrain synthesis. Powered by TCPDF (www.tcpdf.org)