The purpose of this paper is to construct sets, measures and energy forms of certain mixed nested fractals which are spatially homogeneous but not strictly self-similar. We start with the constructions of regular nested fractals, such as Sierpinski gaskets and Koch curves, by employing the iterated map system. Then we show that under the open set condition, the unique invariant (self-similar) measure consists with the normalized Hausdorff measure ristricted on the invariant set. The energy forms construced on regular Sierpinski gaskets and Koch curves is also proved to be a closed form. Next, we use the similar idea, by extending the iterated maps system into a general case, to construct the mixture sets, as well as measures and energy forms. It can be seen that the elements so constructed will not have any strict self-similarity, but them indeed satisfy some weak self-similar properties.

Master of Science / Department of Mathematics / Hrant Hakobyan / When studying geometrical objects less regular than ordinary ones, fractal analysis becomes a valuable tool. Over the last 40 years, this small branch of mathematics has developed extensively. Fractals can be defined as those sets which have non-integer Hausdorff or Minkowski dimension. In this report, we introduce certain definitions of fractal dimensions, which can be used to measure a set’s fractal degree. We introduce Minkowski dimension and Hausdorff dimension and explore some examples where they coincide, as well as other examples where they do not.

“Traces of Wind” is a through-composed work in three movements: "Wind Chimes", "Incantation" and "Meditation". It is scored for a Western sinfonietta ensemble with the addition of a traditional Chinese instrument, guzheng — a 21-stringed traditional Chinese zither, one of the most common instruments of the prominent Chinese musical tradition. In this work, guzheng's role alternates between that of a soloist and of an orchestral instrument. As the piece develops across movements, guzheng takes on a progressively soloistic role: its solo sections become longer and more frequent, with the final movement, "Meditation" being completely a work for guzheng and orchestra. Guzheng's unique sound and obvious reference to the Orient informs the material and orchestration of the work. One hears frequent use of pentatonic scales and imitation of guzheng through Western instruments, such as strings (pizzicati) and harp. Each movement bears an imprint of Chinese music. The opening movement, "Wind Chimes", is based on the idea of repeating pitches, imitating the effect of wind chimes - an attribute of Chinese Feng Shui culture - tossing and bouncing against each other. We hear randomly struck pitches, yet each pitch repeats with a certain regularity. Much of the material of the first movement is derived from an unrelated endeavor: computer programming. I became involved in writing mobile applications for iPhone and Android devices. One year prior to starting my work on "Wind Chimes", I wrote a unique iPhone app, “iSonics”. This app was an attempt to enable performers of electroacoustic music to interact with music physically: a performer prerecords a set of short sounds and taps the empty screen to manipulate these sounds by stretching them in time, pitch-shifting them (by tapping the screen in various locations) and applying various filters by means of tilting the device. I used a guzheng to pre-record a set of 8 different sounds and then improvised a composition. iSonics provided the ability to react to the generated musical material in real time and to inform myself where on the screen to tap next in order to create a convincing musical line. Tapping to the left of the screen rendered the same sound object played slower and at a lower pitch, thus I was able to create harmonies. The first minute of the resultant electroacoustic work is my improvisation of one and the same sound object, while the first minute of "Wind Chimes" is that minute orchestrated for the ensemble, minus the microtones (which are present in the original improvisation). Thus, guzheng being the “pre-recorded” sound serves as the generator of the material for this movement: the original sound object created with guzheng is the foundation of "Wind Chimes". Much of the subsequent material of "Wind Chimes" is derived from the same process of ii instantiating the sound object in different registers and pitch level. Consequently, “striking” this sound object creates complex melodic content, most notably used in the climactic section of the movement (m. 197). "Wind Chimes" flows directly into the second movement, “Incantation”, which is quite different in character, being more dark and dissonant. Spontaneous woodwind passages, which surface throughout, the movement are evocative of the style of singing one hears in a traditional Chinese opera. In the "Meditation", I call for a pair of back-up violins, if available, to perform the opening harmonics section of the movement. The violins are to be retuned to specific microtonal tunings. I carefully selected these tunings by experimenting with various combinations of frequencies with my own violin. Although optional, using microtonal tuning for the opening of the "Meditation" adds a dimension of exoticism to the already Asian-influenced sound world of the complete work.

Identifying finger and wrist flexion based actions using single channel surface electromyogram have a number of rehabilitation, defence and human computer interface applications. These applications are currently infeasible because of unreliability in classification of sEMG when the level of muscle contraction is low and when there are multiple active muscles. The presence of noise and cross-talk from closely located and simultaneously active muscles is exaggerated when muscles are weakly active such as during maintained wrist and finger flexion. It has been established in literature that surface electromyogram (sEMG) and other such biosignals are fractal signals. Some researchers have determined that fractal dimension (FD) is related to strength of muscle contraction. On careful analysis of fractal properties of sEMG, this research work has established that FD is related to the muscle size and complexity and not to the strength of muscle contraction. The work has also identified a novel feature, maximum fractal length (MFL) of the signal, as a good measure of strength of contraction of the muscle. From the analysis, it is observed that while at high level of contraction, root mean square (RMS) is an indicator of strength of contraction of the muscle, this relationship is not very strong when the muscle contraction is less than 50% maximum voluntary contraction. This work has established that MFL is a more reliable measure of strength of contraction compared to RMS, especially at low levels of contraction. This research work reports the use of fractal properties of sEMG to identify the small changes in strength of muscle contraction and the location of the active muscles. It is observed that fractal dimension (FD) of the signal is related with the properties of the muscle while maximum fractal length (MFL) is related to the strength of contraction of the associated muscle. The results show that classifying MFL and FD of a single channel sEMG from the forearm it is possible to accurately identify a set of finger and wrist flexion based actions even when the muscle activity is very weak. It is proposed that such a system could be used to control a prosthetic hand or for human computer interface.

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On assiste depuis quelques années à l'émergence de réseaux de machines, qualifiés de dynamiques, qui ne sont plus limités à une interconnexion de stations de travail définissant un réseau stable. Ces plates-formes intègrent de plus en plus des équipements mobiles et à faibles ressources. L'exploitation effective de ces éseaux dynamiques constitue encore un défi. Du fait de la volatilité des équipements et de leur hétérogénéité, on ne peut avoir une connaissance a priori de toutes les ressources logicielles et matérielles qui sont disponibles dans ces réseaux. De plus, la connectivité entre les différentes machines ne peut être garantie : de nombreux équipements sont régulièrement mis en veille et l'utilisation detechnologie sans fil limite la portée de communication entre les machines. Ces réseaux dynamiques commencent à être exploités pour fournir des applications censées être ubiquitaires, c'est-à-dire des applications dont les fonctionnalités sont accessibles de partout, indépendamment de l'équipement utilisé. Mais de telles applications sont par nature complexes et leur conception est rendue difficile du fait du caractère dynamique des réseaux visés. Le travail décrit dans ce mémoire de thèse a permis de développer des méthodes pour concevoir et déployer des applications ubiquitaires dans des réseaux dynamiques. En nous appuyant sur le modèle de composants Fractal, nous définissons le concept de composants hiérarchiques ubiquitaires, briques d'assemblage des applications ubiquitaires. Un schéma de distribution de ces composants est élaboré afin que ceux-ci puissent offrir leurs services depuis n'importe quelle machine du réseau. Cette distribution des fonctionnalités des composants sur plusieurs machines impose de prendre en compte les déconnexions réseau qui pourraient conduire au dysfonctionnement de l'application. Pour cela, nous avons défini au sein du modèle de composants ubiquitaires le concept d'interface active qui permet de continuer à utiliser certaines parties de l'application tout en isolant celles inutilisables du fait des problèmes de connectivité. Les approches traditionnelles de déploiement ne sont pas adaptées au déploiement des composants ubiquitaires dans les réseaux dynamiques. Dans ces réseaux, les ressources qui sont présentes ne peuvent être connues à l'avance, ce qui empêche la désignation explicite des machines cibles devant héberger les composants. Dans notre approche, le placement des composants est spécifié à l'aide de contraintes exprimant le besoin des composants vis-à-vis des ressources nécessaires à leur exécution. Après avoir présenté un langage permettant la définition de telles contraintes, nous proposons un support intergiciel qui réalise le déploiement d'une application ubiquitaire même si initialement, les ressources exigées par ses composants ne sont pas disponibles et que certaines machines sont inaccessibles. Le processus de déploiement que nous proposons est qualifié de propagatif : les composants sont instanciés au fur et à mesure de la disponibilité des ressources et de l'arrivée des machines. Lorsque des fluctuations de ressources interviennent dans le réseau, les applications ubiquitaires sont amenées à être reconfigurées. La solution que nous présentons permet de rendre ces reconfigurations complètement autonomes, ne nécessitant ainsi plus aucune intervention manuelle. L'ensemble des concepts introduits dans cette thèse a fait l'objet du développement d'un prototype fondé sur une implantation Fractal.

No description available.

It is a research of the move trajectory of the ciliates while feeding the food, in order to estimate, differentiate from the movement behavior under different environments. First, discuss the differently distinguish with the single indicator. Second, discuss with integrate four kinds of indicator whether can distinguish differently. Finally, combine the indicator data and through different analysis technology look out the features of movement behavior, expect to be able to look out suitable information and knowledge from the indicator data. After deal with analytical technology, the result of decision tree is most suitable for predicted and have credibilities. If according to energy of biological, the analysis result is similar to optimal foraging theory. And learn from result under different condition, the movement behavior of the ciliates similar to the optimal foraging theory. In the matter of the result of analysis technology, data of the density of low food similar to data of the density of extremely high food. Besides, data of medium food and high food are analogous. The rule of decision tree can distinguish the density of different food, and can offer follow-up study to distinguish the environmental conditions. Those models are evaluated by predicting accuracies, and rules extracted from decision tree models are also of great help to prediction as well.

Various premixed flame phenomena are studied by means of direct numerical simulations of the complete system of hydrodynamic equations. Rigorous study of flame dynamics is essential for all premixed combustion problems where multidimensional effects cannot be disregarded.The present thesis consists of six parts. The first part deals with the fundamental problem of curved stationary flames propagation in free-slip tubes of different widths. It is shown that only simple "single-hump" slanted stationary flames are possible in tubes wider than some stability limit. The flame dynamics is shown to be governed by a large-scale stability mechanism resulting in a highly slanted flame front.The second part of the thesis is dedicated to studies of acceleration and fractal structure of outward freely propagating flames. It is shown that the development of Landau-Darrieus instability results in the formation of fractal-like flame front structure. Two-dimensional simulation of radially expanding flames displays a radial growth with 1.25 power law temporal behavior. It is shown that the fractal excess for 2D geometry obtained in thenumerical simulation is in good agreement with theoretical predictions.In third part the flame acceleration in tubes with non-slip at the walls is studied in the extremely wide range of flame front velocity. Flame accelerates from small initial velocity to supersonic speed in the laboratory reference frame. Flame acceleration undergoes three stages: 1) initial exponential acceleration in the quasi-isobaric regime, 2) almost linear increase of the flame speed to supersonic values, 3) saturation to a stationary high-speed deflagration velocity, which is correlated with the Chapman-Jouguet deflagration speed. The saturation velocity is in line with previous experimental results.In fourth part the role of viscous stress in heating of the fuel mixture in deflagration-to-detonation transition in tubes is studied both analytically and numerically. The developed analytical theory determines temperature distribution ahead of an accelerating flame. The heating effects of viscous stress and the compression wave become comparable at sufficiently high values of the Mach number. Viscous stress makes heating and explosion of the fuel mixture preferential at the walls.In fifth part we reveal the physical mechanism of ultra-fast flame acceleration in obstructed channels used in modern experiments on detonation triggering. It is demonstrated that delayed burning between the obstacles creates a powerful jet-flow, driving the acceleration. The flame front accelerates exponentially; theanalytical formula for the growth rate is obtained. The theory is validated by extensive direct numerical simulations and comparison to previous experiments.The last part of the thesis concerns the transition from deflagration to detonation. It is found that in sufficiently wide free-slip channels and for sufficiently fast flames Landau-Darrieus instability may invoke nucleation of hot spots within the wrinkled flame folds, triggering an abrupt transition from deflagrative to detonative combustion. Results on DDT in channels with non-slip at the walls are also presented. / QC 20100915

This thesis presents two novel coding schemes and applications to both two- and three-dimensional image compression. Image compression can be viewed as methods of functional approximation under a constraint on the amount of information allowable in specifying the approximation. Two methods of approximating functions are discussed: Iterated function systems (IFS) and wavelet-based approximations. IFS methods approximate a function by the fixed point of an iterated operator, using consequences of the Banach contraction mapping principle. Natural images under a wavelet basis have characteristic coefficient magnitude decays which may be used to aid approximation. The relationship between quantization, modelling, and encoding in a compression scheme is examined. Context based adaptive arithmetic coding is described. This encoding method is used in the coding schemes developed. A coder with explicit separation of the modelling and encoding roles is presented: an embedded wavelet bitplane coder based on hierarchical context in the wavelet coefficient trees. Fractal (spatial IFSM) and fractal-wavelet (coefficient tree), or IFSW, coders are discussed. A second coder is proposed, merging the IFSW approaches with the embedded bitplane coder. Performance of the coders, and applications to two- and three-dimensional images are discussed. Applications include two-dimensional still images in greyscale and colour, and three-dimensional streams (video).