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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
241

On non-archimedean dynamical systems

Joyner, Sheldon T 12 1900 (has links)
Thesis (MSc) -- University of Stellenbosch, 2000. / ENGLISH ABSTRACT: A discrete dynamical system is a pair (X, cf;) comprising a non-empty set X and a map cf; : X ---+ X. A study is made of the effect of repeated application of cf; on X, whereby points and subsets of X are classified according to their behaviour under iteration. These subsets include the JULIA and FATOU sets of the map and the sets of periodic and preperiodic points, and many interesting questions arise in the study of their properties. Such questions have been extensively studied in the case of complex dynamics, but much recent work has focussed on non-archimedean dynamical systems, when X is projective space over some field equipped with a non-archimedean metric. This work has uncovered many parallels to complex dynamics alongside more striking differences. In this thesis, various aspects of the theory of non-archimedean dynamics are presented, with particular reference to JULIA and FATOU sets and the relationship between good reduction of a map and the empty JULIA set. We also discuss questions of the finiteness of the sets of periodic points in special contexts. / AFRIKAANSE OPSOMMING: 'n Paar (X, <jJ) bestaande uit 'n nie-leë versameling X tesame met 'n afbeelding <jJ: X -+ X vorm 'n diskrete dinamiese sisteem. In die bestudering van so 'n sisteem lê die klem op die uitwerking op elemente van X van herhaalde toepassing van <jJ op die versameling. Elemente en subversamelings van X word geklasifiseer volgens dinamiese kriteria en op hierdie wyse ontstaan die JULIA en FATOU versamelings van die afbeelding en die versamelings van periodiese en preperiodiese punte. Interessante vrae oor die eienskappe van hierdie versamelings kom na vore. In die geval van komplekse dinamika is sulke vrae reeds deeglik bestudeer, maar onlangse werk is op nie-archimediese dinamiese sisteme gedoen, waar X 'n projektiewe ruimte is oor 'n liggaam wat met 'n nie-archimediese norm toegerus is. Hierdie werk het baie ooreenkomste maar ook treffende verskille met die komplekse dinamika uitgewys. In hierdie tesis word daar ondersoek oor verskeie aspekte van die teorie van nie-archimediese dinamika ingestel, in besonder met betrekking tot die JULIA en FATOU versamelings en die verband tussen goeie reduksie van 'n afbeelding en die leë JULIA versameling. Vrae oor die eindigheid van versamelings van periodiese punte in spesiale kontekste word ook aangebied.
242

Boolean functions and discrete dynamics: analytic and biological application

Ebadi, Haleh 05 July 2016 (has links) (PDF)
Modeling complex gene interacting systems as Boolean networks lead to a significant simplification of computational investigation. This can be achieved by discretization of the expression level to ON or OFF states and classifying the interactions to inhibitory and activating. In this respect, Boolean functions are responsible for the evolution of the binary elements of the Boolean networks. In this thesis, we investigate the mostly used Boolean functions in modeling gene regulatory networks. Moreover, we introduce a new type of function with strong inhibitory namely the veto function. Our computational and analytic studies on the verity of the networks capable of constructing the same State Transition Graph lead to define a new concept namely the “degeneracy” of Boolean functions. We further derive analytically the sensitivity of the Boolean functions to perturbations. It turns out that the veto function forms the most robust dynamics. Furthermore, we verify the applicability of veto function to model the yeast cell cycle networks. In particular, we show that in an intracellular signal transduction network [Helikar et al, PNAS (2008)], the functions with veto are over-represented by a factor exceeding the over-representation of threshold functions and canalyzing functions in the same system. The statistics of the connections of the functional networks are studied in detail. Finally, we look at a different scale of biological phenomena using a binary model. We propose a simple correlation-based model to describe the pattern formation of Fly eye. Specifically, we model two different procedures of Fly eye formation, and provide a generic approach for Fly eye simulation.
243

Two Generalizations of the Filippov Operation

Eryuzlu, Menevse 01 April 2016 (has links)
The purpose of this thesis is to generalize Filippov's operation, and to get more useful results. It includes two main parts: The C-Filippov operation for the finite and countable cases and the Filippov operation with different measures. In the first chapter, we give brief information about the importance of Filippov's operation, our goal and the ideas behind our generalizations. In the second chapter, we give some sufficient background notes. In the third chapter, we introduce the Filippov operation, explain how to calculate the Filippov of a function and give some sufficient properties of it. In the fourth chapter, we introduce a generalization of the Filippov operation, the C-Filippov, and give some of its properties which we need for the next chapter. In the fifth chapter, in the first main part, we discuss some properties of the C-Filippov for special cases and observe the differences and common properties between the Filippov and C-Filippov operations. Finally, in the sixth chapter, we present the other generalization of the Filippov operation which is Filippov with different measures. We observe the properties of the corresponding Filippovs when we know the relationship between the measures. We finish the thesis by summarizing our work and discussing future work.
244

COORDINATION OF SWIMBENCH FREESTYLE IN ELITE AND NON-ELITE SWIMMERS: A DYNAMICAL SYSTEM APPROACH

Spigelman, Tracy H. 01 January 2009 (has links)
Elite swimmers can be distinguished from novice swimmers by freestyle stroke technique. Elite swimmers move through multiple coordination modes, increases in stroke lengths, stroke rates, and body roll allowing for a more symmetrical stroke and increased speed compared with novice swimmer during 100m freestyle. Coaches strive to improve swimmers’ performance by providing feedback about stroke technique, mostly from the pool deck where view of the full stroke cycle is obstructed by the water. Tools to assess swimming are often expensive and require extra training, which does not provide a pragmatic solution. A dryland rotational swimbench would provide a means to evaluate freestyle swimming. The aim of the present study is to evaluate the sensory motor system of elite and novice level swimmers by comparing kinematic, coordinative structures and spatial-temporal characteristics of freestyle stroke on a dryland swimbench with a rotational component. Thirty elite and novice collegiate and masters swimmers were instrumented with reflective markers bilaterally on the upper extremity and torso. A series of four ten second trials of freestyle sprint swimming were performed on the swimbench. Repeated measures were used for statistical analysis for comparison between and within groups. Bonferroni corrections were used as post-hoc analysis. Results indicated no significant difference between elite and novice swimmers’ sensory-motor system, kinematics or spatio-temporal systems on a rotational swimbench. Similarities could be accounted for by swimmers perceiving a novel task due to differences in sensory feedback, and mechanical limitations of the bench. It is noteworthy that catch-up/opposition coordination are more common than superposition which provides support for the swimbench providing a more similar representation to in water swimming.
245

Contribution à l'identification fréquentielle robuste des systèmes dynamiques linéaires

Torkhani, Nabil 04 December 1995 (has links) (PDF)
Cette thèse concerne le problème d'identification robuste H indice infini de données harmoniques sur une bande limitée de fréquence, généralisation plus réaliste du problème d'identification robuste H indice infini étudié ces dernières années notamment par Gu, Helmiki, Jacobson, Kargonekhar, Mäkilä, Nett et Partington. L'introduction, en dehors de cette bande, d'un comportement de référence et d'un gabarit rend possible une adaptation des algorithmes classiques en deux étapes, La solution du problème posé est alors donnée par la résolution d'un problème extrémal borné après une première étape d'interpolation robuste des données sur un arc du cercle unité. Cependant, la solution ainsi calculée est typiquement discontinue. La principale contribution de ce travail à l'identification fréquentielle robuste consiste à montrer qu'il est possible de prendre en compte le caractère local des données en fréquence et garantir l'appartenance de la solution à l'algèbre du disque. Un algorithme est donné et sa mise en œuvre numérique est détaillée. Le choix du comportement en dehors de la bande considérée pose plus généralement le problème de complétion analytique borné dans H indice p. Nous le résolvons dans H indice 2 et l'utiliserons pour vérifier la validité de l'hypothèse de linéarité du système.
246

Pathwise properties of random quadratic mapping

Lian, Peng January 2010 (has links)
No description available.
247

Well-posedness of dynamics of microstructure in solids

Sengul, Yasemin January 2010 (has links)
In this thesis, the problem of well-posedness of nonlinear viscoelasticity under the assumptions allowing for phase transformations in solids is considered. In one space dimension we prove existence and uniqueness of the solutions for the quasistatic version of the model using approximating sequences corresponding to the case when initial data takes finitely many values. This special case also provides upper and lower bounds for the solutions which are interesting in their own rights. We also show equivalence of the existence theory we develop with that of gradient flows when the stored-energy function is assumed to be -convex. Asymptotic behaviour of the solutions as time goes to infinity is then investigated and stabilization results are obtained by means of a new argument. Finally, we look at the problem from the viewpoint of curves of maximal slope and follow a time-discretization approach. We introduce a three-dimensional method based on composition of time-increments, as a result of which we are able to deal with the physical requirement of frame-indifference. In order to test this method and distinguish the difficulties for possible generalizations, we look at the problem in a convex setting. At the end we are able to obtain convergence of the minimization scheme as time step goes to zero.
248

Winnerless competition in neural dynamics : cluster synchronisation of coupled oscillators

Wordsworth, John January 2009 (has links)
Systems of globally coupled phase oscillators can have robust attractors that are heteroclinic networks. Such a heteroclinic network is generated, where the phases cluster into three groups, within a specific regime of parameters when the phase oscillators are globally coupled using the function $g(\varphi) = -\sin(\varphi + \alpha) + r \sin(2\varphi + \beta)$. The resulting network switches between 30 partially synchronised states for a system of $N=5$ oscillators. Considering the states that are visited and the time spent at those states a spatio-temporal code can be generated for a given navigation around the network. We explore this phenomenon further by investigating the effect that noise has on the system, how this system can be used to generate a spatio-temporal code derived from specific inputs and how observation of a spatio-temporal code can be used to determine the inputs that were presented to the system to generate a given coding. We show that it is possible to find chaotic attractors for certain parameters and that it is possible to detail a genetic algorithm that can find the parameters required to generate a specific spatio-temporal code, even in the presence of noise. In closing we briefly explore the dynamics where $N&gt;5$ and discuss this work in relation to winnerless competition.
249

Modèle computationnel d'attention pour la vision adaptative / Computational attention model for adaptive vision

Perreira da Silva, Matthieu 10 December 2010 (has links)
L'analyse temps réel de la masse de données générée par les mécanismes de gestion de la vision dans les applications interactives est un problème toujours ouvert, promettant des avancées importantes dans des domaines aussi variés que la robotique, l’apprentissage à distance ou les nouvelles formes d’interactions avec l’utilisateur, sans clavier ni souris. Dans le cadre général de la vision, les algorithmes d’analyse de scène doivent trouver un compromis entre d'une part la qualité des résultats recherchés et d'autre part la quantité de ressources allouable aux différents tâches. Classiquement, ce choix est effectué à la conception du système (sous la forme de paramètres et d’algorithmes prédéfinis), mais cette solution limite le champ d’application de celui-ci. Une solution plus flexible consiste à utiliser un système de vision adaptatif qui pourra modifier sa stratégie d’analyse en fonction des informations disponibles concernant son contexte d’exécution. En conséquence, ce système doit posséder un mécanisme permettant de guider rapidement et efficacement l’exploration de la scène afin d’obtenir ces informations. Chez l’homme, les mécanismes de l’évolution ont mis en place le système d’attention visuelle. Ce système sélectionne les informations importantes afin de réduire la charge cognitive et les ambiguïtés d’interprétation de la scène. Nous proposons, dans cette thèse, un système d'attention visuelle, dont nous définissons l’architecture et les principes de fonctionnement. Ce dernier devra permettre l’interaction avec un système de vision afin qu’il adapte ses traitements en fonction de l’intérêt de chacun des éléments de la scène, i.e. ce que nous appelons saillance. A la croisée des chemins entre les modèles centralisés et hiérarchiques (ex : [Koch1985], puis [Itti1998]), et les modèles distribués et compétitifs (ex : [Desimone1995], puis [Deco2004, Rolls2006]), nous proposons un modèle hiérarchique, compétitif et non centralisé. Cette approche originale permet de générer un point de focalisation attentionnel à chaque pas de temps sans utiliser de carte de saillance ni de mécanisme explicite d’inhibition de retour. Ce nouveau modèle computationnel d'attention visuelle temps réel est basé sur un système d'équations proies / prédateurs, qui est bien adapté pour l'arbitrage entre un comportement attentionnel non déterministe et des propriétés de stabilité, reproductibilité, et réactivité. L'analyse des expérimentations menées est positive : malgré le comportement non-déterministe des équations proies / prédateurs, ce système possède des propriétés intéressantes de stabilité, reproductibilité, et réactivité, tout en permettant une exploration rapide et efficace de la scène. Ces propriétés ouvrent la possibilité d’aborder différents types d’applications allant de l’évaluation de la complexité d’images et de vidéos à la détection et au suivi d’objets. Enfin, bien qu’il soit destiné à la vision par ordinateur, nous comparons notre modèle au système attentionnel humain et montrons que celui-ci présente un comportement aussi plausible (voire plus en fonction du comportement défini) que les modèles classiques existants. / Providing real time analysis of the huge amount of data generated by computer vision algorithms in interactive applications is still an open problem. It promises great advances across a wide variety of fields : robotics, distance education, or new mouse-less and keyboard-less human computer interaction.When using scene analysis algorithms for computer vision, a trade-off must be found between the quality of the results expected, and the amount of computer resources allocated for each task. It is usually a design time decision, implemented through the choice of pre-defined algorithms and parameters. However, this way of doing limits the generality of the system. Using an adaptive vision system provides a more flexible solution as its analysis strategy can be changed according to the information available concerning the execution context. As a consequence, such a system requires some kind of guiding mechanism to explore the scene faster and more efficiently.In human, the mechanisms of evolution have generated the visual attention system which selects the most important information in order to reduce both cognitive load and scene understanding ambiguity.In this thesis, we propose a visual attention system tailored for interacting with a vision system (whose theoretical architecture is given) so that it adapts its processing according to the interest (or salience) of each element of the scene.Somewhere in between hierarchical salience based (ex: [Koch1985], then [Itti1998]) and competitive distributed (ex: [Desimone1995], then [Deco2004, Rolls2006]) models, we propose a hierarchical yet competitive and non salience based model. Our original approach allows the generation of attentional focus points without the need of neither saliency map nor explicit inhibition of return mechanism. This new real-time computational model is based on a preys / predators system. The use of this kind of dynamical system is justified by an adjustable trade-off between nondeterministic attentional behavior and properties of stability, reproducibility and reactiveness.Our experiments shows that despite the non deterministic behavior of preys / predators equations, the system exhibits interesting properties of stability, reproducibility and reactiveness while allowing a fast and efficient exploration of the scene. These properties are useful for addressing different kinds of applications, ranging from image complexity evaluation, to object detection and tracking. Finally, while it is designed for computer vision, we compare our model to human visual attention. We show that it is equally as plausible as existing models (or better, depending on its configuration).
250

Dynamical system decomposition and analysis using convex optimization

Anderson, James David January 2012 (has links)
This thesis is concerned with investigating new methods for the analysis of large-scale dynamical systems using convex optimization. The proposed methodology is based on composite Lyapunov theory and is computationally implemented using polynomial programming techniques. The main result of this work is the development of a system decomposition framework that makes it possible to analyze systems that are of such a scale that traditional methods cannot cope with. We begin by addressing the problem of model invalidation. A barrier certificate method for invalidating models in the presence of uncertain data is presented for both continuous and discrete time models. It is shown how a re-parameterization of the time dependent variables can improve the numerical conditioning of the underlying optimization problem. The main contribution of this thesis is the development of an automated dynamical system decomposition framework that permits us to verify the stability of systems that typically have a state dimension large enough to render traditional computational methods intractable. The underlying idea is to decompose a system into a set of lower order subsystems connected in feedback in such a manner that composite methods for stability verification may be employed. What is unique about the algorithm presented is that it takes into account both dynamics and the topology of the interconnection graph. In the first instance we illustrate the methodology with an ecological network and primal Internet congestion control scheme. The versatility of the decomposition framework is also highlighted when it is shown that when applied to a model of the EGF-MAPK signaling pathway it is capable of identifying biologically relevant subsystems in addition to stability verification. Finally we introduce stability metrics for interconnected dynamical systems based on the theory of dissipativity. We conclude by outlining a clustering based decomposition algorithm that explicitly takes into account the input and output dynamics when determining the system decomposition.

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