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D'Ambros, Paola. "Algebraic dynamics in positive characteristic." Thesis, University of East Anglia, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.365044.
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Virili, Simone. "Group representations, algebraic dynamics and torsion theories." Doctoral thesis, Universitat Autònoma de Barcelona, 2014. http://hdl.handle.net/10803/284141.
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La tesis está organizada en doce capítulos, divididos en cinco partes. La Parte I comprende los primeros tres capítulos. En el Capítulo 1 damos una breve introducción a la teoría de las categorías y recordamos las técnicas de las teorías de torsión y de la localización de categorías de Grothendieck. Empezamos el Capítulo 2 introduciendo la categoría de los "casi-frames" y estudiamos algunas construcciones básicas en esta categoría; en la segunda parte del capítulo estudiamos las dimensiones de Krull y de Gabriel de los casi-frames. Usando el hecho que los retículos de sub-objectos de un objeto dado en una categoría de Grothendieck es un casi-frame, podemos re-definir las nociones clásicas de dimension de Krull y de Gabriel para estos objetos. En el Capítulo 3 damos una breve introducción a los grupos y módulos topológicos. En particular, enunciamos el Teorema de Dualidad de Pontryagin-Van Kampen y el Teorema de Inversión de Fourier; además damos una demostración completa de un caso particular del Teorema de Dualidad de Müller entre módulos discretos y estrictamente linealmente compactos. Le Parte II está dedicada al estudio de la entropía en un contexto categórico. En el Capítulo 4 introducimos la categoría de los semigroupos pre-normados y la categoría de las T-representaciones de un monoide T sobre una categoría dada. Entonces definimos y estudiamos una función de entropía en la categoría de las T-representaciones sobre la categoría de los semigrupos pre-normados, con mayor énfasis en el caso en que T es un grupo amenable. En el Capítulo 5 damos ejemplos de invariantes clásicos que se pueden obtener de forma funtorial usando la entropía de semigrupos pre-normados definida en el capítulo anterior. Finalmente en el Capítulo 6 demostramos un Teorema Puente que relaciona la entropía topológica de acciones sobre grupos localmente compactos abelianos con la entropía algebraica de la acción sobre el grupo dual. En la Parte III estudiamos el problema de la extensión de las funciones de longitud a clases de módulos sobre productos cruzados utilizando la entropía. En particular, en el Capítulo 7 demostramos un teorema que describe la estructura de todas las funciones de longitud de una categoría de Grothendieck con dimensión de Gabriel. En el Capítulo 8 definimos y estudiamos la L-entropía algebraica de un RfiG-módulo M por la izquierda, donde R en un anillo general, G en un grupo amenable numerable y L es una función de longitud. En la Parte IV aplicamos la teoría desarollada a lo largo de la tesis a algunas conjeturas clásicas de la teoría de representaciones de grupos: la \Surjunctivity Conjecture", la \L-Surjunctivity Conjecture", la \Stable Finiteness Conjecture" y la \Zero-Divisors Conjecture". En el Capítulo 9 describimos las conjeturas y algunas relaciones entre ellas, inducidas por la dualidad de Müller. En el Capítulo 10 nos centramos en el caso amenable de las conjeturas, utilizando la entropía topologica para demostrar la Surjunctivity Conjecture para grupos amenables. Además explotamos la L-entropía algebraica para estudiar una versión general de la Stable Finiteness Conjecture y de la Zero-Divisors Conjecture. En el Capítulo 11 nos centramos en el caso sóficio de la L-Surjunctivity Conjecture y de la Stable Finiteness Conjecture, reduciendo ambas conjeturas a un enunciado más general sobre endomorfismos de casi-frames. Esto nos permite extender los resultados conocidos hasta ahora sobre las dos conjeturas. La Parte V está dedicada al estudio de aproximaciones de modelos para el algebra homológica relativa. En particular, aplicamos las herramientas desarrolladas en los Capítulos 1 y 2 para generalizar y re-interpretar algunos resultados recientes de Chachólski, Neeman, Pitsch, y Scherer.The thesis is organized in twelve chapters divided in five parts. Part I encompasses the first three chapters and consists mainly of background material. In Chapter 1 we provide the necessary background in general category theory and we recall the machinery of torsion theories and localization of Grothendieck categories. We start Chapter 2 introducing the category of quasi-frame and we study the basic constructions in this category. In the second part of the chapter we study the Krull and the Gabriel dimension of quasi-frames. Using the fact that the poset of sub-objects of a given object in a Grothendieck category is a quasi-frame, we re-obtain the classical notions of Krull and Gabriel dimension for such objects. In Chapter 3 we provide the necessary background in topological groups and modules. In particular, we state the Pontryagin-Van Kampen Duality Theorem and the Fourier Inversion Theorem, furthermore we give a complete proof of a particular case of the Mülcer Duality Theorem between discrete and strictly linearly compact modules. Part II is devoted to the study of entropy in a categorical setting. In Chapter 4 we introduce the category of pre-normed semigroups and the category of left T-representations of a monoid T over a given category. Then, we introduce and study an entropy function in the category of left T-representations over the category of normed-semigroups, with particular emphasis on the case when T is an amenable group. Chapter 5 consist of a series of examples of classical invariants that can be obtained functorially using the entropy of pre-normed semigroups. Finally, in Chapter 6 we prove a Bridge Theorem that connects the topological entropy of actions on locally compact Abelian groups to the algebraic entropy of the action induced on the dual group. Part III is devoted to the study of length functions and to apply the machinery of entropy to extend length functions to crossed products. Indeed, in Chapter 7 we prove a general structure theorem for length functions of Grothendieck categories with Gabriel dimension. In Chapter 8 we define the algebraic L-entropy of a left RfiG-module M, where R is a general ring and G is a countable amenable group and L is a suitable length function. In Part IV we apply the theory developed in the three previous parts to some classical conjectures in group representations: the Surjunctivity Conjecture, the L-Surjunctivity Conjecture, the Stable Finiteness Conjecture and the Zero-Divisors Conjecture. Using the Müller Duality Theorem we can clarify some relations among these conjectures. In Chapter 10 we concentrate on the amenable case of the above conjectures. In particular, we show how to use topological entropy to prove the Surjunctivity Conjecture for amenable groups and we use the algebraic L-entropy to study (general versions of) the Stable Finiteness and the Zero-Divisors Conjectures. In Chapter 11 we concentrate on the sofic case of the L-Surjunctivity and of the Stable Finiteness Conjectures. In particular, we reduce both conjectures to a more general statement about endomorphisms of quasi-frames. This allows us to generalize the known results on both conjectures. Finally, Part V is devoted to the study of model approximations for relative homological algebra. In particular, we apply the machinery introduced in Chapters 1 and 2 to extend and reinterpret some recent results of Chachfiolski, Neeman, Pitsch, and Scherer.
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Wendler, Tim Glenn. "Algebraic Semi-Classical Model for Reaction Dynamics." BYU ScholarsArchive, 2014. https://scholarsarchive.byu.edu/etd/5755.
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We use an algebraic method to model the molecular collision dynamics of a collinear triatomic system. Beginning with a forced oscillator, we develop a mathematical framework upon which inelastic and reactive collisions are modeled. The model is considered algebraic because it takes advantage of the properties of a Lie algebra in the derivation of a time-evolution operator. The time-evolution operator is shown to generate both phase-space and quantum dynamics of a forced oscillator simultaneously. The model is considered semi-classical because only the molecule's internal degrees-of-freedom are quantized. The relative translation between the colliding atom and molecule in an exchange reaction (AB+C ->A+BC) contains no bound states and any possible tunneling is neglected so the relative translation is treated classically. The purpose of this dissertation is to develop a working model for the quantum dynamics of a collinear reactive collision. After a reliable model is developed we apply statistical mechanics principles by averaging collisions with molecules in a thermal bath. The initial Boltzmann distribution is of the oscillator energies. The relative velocities of the colliding particles is considered a thermal average. Results are shown of quantum transition probabilities around the transition state that are highly dynamic due to the coupling between the translational and transverse coordinate.
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Xie, Junyi. "Algebraic dynamics of rational self-maps on surfaces." Palaiseau, Ecole polytechnique, 2014. http://pastel.archives-ouvertes.fr/docs/01/02/54/12/PDF/phd20140412.pdf.
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Cette thèse se se compose de trois parties. La première partie est consacrée à l'étude des points périodiques des applications birationnelles des surfaces projectives. Nous montrons que toute application birationnelle de surface dont la croissance des degrés est exponentielle admet un ensemble de points périodiques Zariski dense. Dans la seconde partie, nous démontrons la conjecture de Mordell-Lang dynamique pour toute application polynomiale birationnelle du plan affine définie sur un corps de caractéristique nulle. Notre approche donne une nouvelle démonstration de cette conjecture pour les automorphismes polynomiaux du plan. Enfin la troisième partie porte sur un problème de géométrie affine inspiré par la généralisation au cas de toutes les applications polynomiales du plan affine de la conjecture de Mordell-Lang dynamique. Etant donné un ensemble fini S de valuations sur l'anneau de polynomes k[x,y] sur un corps algébriquement clos k triviales sur k, nous donnons une condition nécessaire et suffisante pour que le corps des fractions de l'intersection des anneaux de valuations de S avec k[x,y] soit de degré de transcendance 2 sur kThis thesis contains three parts. The first one is devoted to the study of the set of periodic points for birational surface maps. We prove that any birational transformation of a smooth projective surface whose degree growth is exponential admits a Zariski-dense set of periodic orbits. In the second part, we prove the dynamical Mordell-Lang conjecture for all polynomial birational transformations of the affine plane defined over a field of characteristic zero. Our approach gives a new proof of this conjecture for polynomial automorphisms of the affine plane. The last part is concerned with a problem in affine geometry that was inspired by the generalization to any polynomial map of the dynamical Mordell-Lang conjecture. Given any finite set S of valuations that are defined on the polynomial ring k[x,y] over an algebraically closed field k, trivial on k, we give a necessary and sufficient condition so that the field of fractions of the intersection of the valuation rings of S with k[x,y] has transcendence degree 2 over k
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Alam, Md Shafiful. "Iterative Methods to Solve Systems of Nonlinear Algebraic Equations." TopSCHOLAR®, 2018. https://digitalcommons.wku.edu/theses/2305.
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Iterative methods have been a very important area of study in numerical analysis since the inception of computational science. Their use ranges from solving algebraic equations to systems of differential equations and many more. In this thesis, we discuss several iterative methods, however our main focus is Newton's method. We present a detailed study of Newton's method, its order of convergence and the asymptotic error constant when solving problems of various types as well as analyze several pitfalls, which can affect convergence. We also pose some necessary and sufficient conditions on the function f for higher order of convergence. Different acceleration techniques are discussed with analysis of the asymptotic behavior of the iterates. Analogies between single variable and multivariable problems are detailed. We also explore some interesting phenomena while analyzing Newton's method for complex variables.
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Jogia, Danesh Michael Mathematics & Statistics Faculty of Science UNSW. "Algebraic aspects of integrability and reversibility in maps." Publisher:University of New South Wales. Mathematics & Statistics, 2008. http://handle.unsw.edu.au/1959.4/40947.
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We study the cause of the signature over finite fields of integrability in two dimensional discrete dynamical systems by using theory from algebraic geometry. In particular the theory of elliptic curves is used to prove the major result of the thesis: that all birational maps that preserve an elliptic curve necessarily act on that elliptic curve as addition under the associated group law. Our result generalises special cases previously given in the literature. We apply this theorem to the specific cases when the ground fields are finite fields of prime order and the function field $mathbb{C}(t)$. In the former case, this yields an explanation of the aforementioned signature over finite fields of integrability. In the latter case we arrive at an analogue of the Arnol'd-Liouville theorem. Other results that are related to this approach to integrability are also proven and their consequences considered in examples. Of particular importance are two separate items: (i) we define a generalization of integrability called mixing and examine its relation to integrability; and (ii) we use the concept of rotation number to study differences and similarities between birational integrable maps that preserve the same foliation. The final chapter is given over to considering the existence of the signature of reversibility in higher (three and four) dimensional maps. A conjecture regarding the distribution of periodic orbits generated by such maps when considered over finite fields is given along with numerical evidence to support the conjecture.
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Berger, Ulrich. "Non-algebraic convergence proofs for continuous-time fictitious play." Springer, 2012. http://epub.wu.ac.at/5591/1/2012_DGA.pdf.
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In this technical note we use insights from the theory of projective geometry to provide novel and non-algebraic proofs of convergence of continuous-time fictitious play for a class of games. As a corollary we obtain a kind of equilibrium selection result, whereby continuous-time fictitious play converges to a particular equilibrium contained in a continuum of equivalent equilibria for symmetric 4x4 zero-sum games.
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D'Rozario, Robert S. G. "Conformational dynamics of proline-containing transmembrane helices." Thesis, University of Oxford, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.670181.
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Mirahmadi, Marjansadat [Verfasser]. "Spectra and Dynamics of Driven Linear Quantum Rotors: Symmetry Analysis and Algebraic Methods / Marjansadat Mirahmadi." Berlin : epubli, 2020. http://d-nb.info/1205608095/34.
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Müller, Annette [Verfasser]. "On algebraic and geometric aspects of fluid dynamics: New perspectives based on Nambu mechanics and its applications to atmospheric dynamics / Annette Müller." Berlin : Freie Universität Berlin, 2018. http://d-nb.info/117670544X/34.
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Tschirhart, Hugo. "From two Algebraic Bethe Ansätze to the dynamics of Dicke-Jaynes-Cummings-Gaudin quantum integrable models through eigenvalue-based determinants." Thesis, Université de Lorraine, 2017. http://www.theses.fr/2017LORR0098/document.
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Le travail présenté dans cette thèse est inspiré de précédents résultats sur les modèles de Gaudin ne contenant que des spins-1/2 (ces modèles sont intégrables) qui, par un changement de variable dans les équations de Bethe algébriques, parviennent à simplifier le traitement numérique de ces modèles. Cette optimisation numérique s'effectue par l'intermédiaire d'une construction en déterminant, ne dépendant que des variables précédemment mentionnées, pour chaque produit scalaire intervenant dans l'expression de la moyenne d'une observable à un temps donné. En montrant qu'il est possible d'utiliser la méthode du Quantum Inverse Scattering Method (QISM), même dans un cas où l'état du vide n'est pas état propre de la matrice de transfert, les résultats précédents concernant uniquement des spins-1/2 sont généralisés à des modèles contenant en plus une interaction spin-boson. De fait, cette généralisation a ouvert plusieurs voies de recherche possibles. Premièrement, il est montré qu'il est possible de continuer à généraliser l'utilisation de déterminants pour des modèles de spins décrivant l'interaction d'un spin de norme arbitraire avec des spins-1/2. La méthode permettant d'obtenir la construction des expressions explicites de ces déterminants est donnée. On peut également pousser la généralisation à d'autres modèles de Gaudin dont l'état du vide n'est pas état propre de la matrice de transfert. C'est ce que nous avons fait pour des spins-1/2 en interaction avec un champ magnétique dont l'orientation est arbitraire. Enfin, un traitement numérique de ces systèmes de spins-1/2 interagissant avec un mode bosonique est présenté. L'évolution temporelle de l'occupation bosonique et de l'aimantation locale des spins est ainsi étudiée selon deux Hamiltoniens différents, l'Hamiltonien de Tavis-Cummings et un Hamiltonien type spin central. Cette étude nous apprend que la dynamique de ces systèmes, qui relaxent d'un état initial vers un état stationnaire, conduit à un état superradiant lorsque l'état initial choisi y est favorableThe work presented in this thesis was inspired by precedent results on the Gaudin models (which are integrable) for spins-1/2 only which, by a change of variables in the algebraic Bethe equations, manage to considerably simplify the numerical treatment of such models. This numerical optimisation is carried out by the construction of determinants, only depending on the previously mentioned variables, for every scalar products appearing in the expression of the mean value of an observable of interest at a given time. By showing it is possible to use the Quantum Inverse Scattering Method (QISM), even when the vacuum state is not eigenstate of the transfer matrix, the previous results concerning spins-1/2 only are generalised to models including an additional spin-boson interaction. De facto, this generalisation opened different possible paths of research. First of all, we show that it is possible to further generalise the use of determinants for spin models describing the interaction of one spin of arbitrary norm with many spins-1/2. We give the method leading to the explicit construction of determinants’ expressions. Moreover, we can extend this work to other Gaudin models where the vacuum state is not an eigenstate of the transfer matrix. We did this work for spins-1/2 interacting with an arbitrarily oriented magnetic field. Finally, a numerical treatment of systems describing the interaction of many spins-1/2 with a single bosonic mode is presented. We study the time evolution of bosonic occupation and of local magnetisation for two different Hamiltonians, the Tavis-Cummings Hamiltonian and a central spin Hamiltonian. We learn that the dynamics of these systems, relaxing from an initial state to a stationary state, leads to a superradiant-like state for certain initial states
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Tschirhart, Hugo. "From two algebraic Bethe Ansätze to the dynamics of Dicke-Jaynes-Cummings-Gaudin quantum integrable models through eigenvalue-based determinants." Thesis, Coventry University, 2017. http://curve.coventry.ac.uk/open/items/ee00088e-9dd9-4709-8974-9ef528fda6f4/1.
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The work presented in this thesis was inspired by precedent results on the Gaudin models (which are integrable) for spins-12 only which, by a change of variables in the algebraic Bethe equations, manage to considerably simplify the numerical treatment of such models. This numerical optimisation is carried out by the construction of determinants, only depending on the previously mentioned variables, for every scalar products appearing in the expression of the mean value of an observable of interest at a given time. By showing it is possible to use the Quantum Inverse ScatteringMethod (QISM), even when the vacuum state is not eigenstate of the transfer matrix, the previous results concerning spins-12 only are generalised tomodels including an additional spin-boson interaction. De facto, this generalisation opened different possible paths of research. First of all, we show that it is possible to further generalise the use of determinants for spin models describing the interaction of one spin of arbitrary normwith many spins-12. We give the method leading to the explicit construction of determinants’ expressions. Moreover, we can extend this work to other Gaudin models where the vacuumstate is not an eigenstate of the transfer matrix. We did this work for spins-12interacting with an arbitrarily oriented magnetic field. Finally, a numerical treatment of systems describing the interaction ofmany spins-12 with a single bosonic mode is presented. We study the time evolution of bosonic occupation and of local magnetisation for two different Hamiltonians, the Tavis-Cummings Hamiltonian and a central spin Hamiltonian. We learn that the dynamics of these systems, relaxing from an initial state to a stationary state, leads to a superradiant-like state for certain initial states.
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Mirahmadi, Marjansadat [Verfasser], Burkhard [Gutachter] Schmidt, Bretislav [Gutachter] Friedrich, and Olga [Gutachter] Smirnova. "Spectra and dynamics of driven linear quantum rotors : symmetry analysis and algebraic methods / Marjansadat Mirahmadi ; Gutachter: Burkhard Schmidt, Bretislav Friedrich, Olga Smirnova." Berlin : Technische Universität Berlin, 2020. http://d-nb.info/1206637471/34.
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Dang, Nguyen-Bac. "Croissance des degrés d'applications rationnelles en dimension 3." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLX044/document.
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Cette thèse comporte trois chapitres indépendants portant sur l’itération des applicationsrationnelles sur des variétés projectives et plus spécifiquement sur l’étude du comportement dela suite des degrés des itérés de telles applications.Dans le premier chapitre, nous donnons une construction des invariants fondamentaux quesont les degrés dynamiques dans un cadre très général, et ce sans hypothèse ni sur la caractéristique ni sur les singularités de l’espace ambiant. Cette construction repose sur des propriétésde positivité des cycles algébriques, et propose une alternative aux approches analytiques deDinh et Sibony ou algébriques de Truong.Le second chapitre est issu d’un article écrit en commun avec Jian Xiao. Notre contributionporte sur des objets centraux en géométrie convexe appelés valuations. Nous transférons à l’espace des valuations des notions de positivité des cycles algébriques récemment introduites parLehmann et Xiao, ce qui nous permet d’étendre l’opération de convolution originellement définie par Bernig et Fu à une sous-classe de valuations suffisamment positives.Le troisième chapitre constitue le coeur de la thèse, et porte sur des estimations des degrésdynamiques des automorphismes dit modérés de la quadrique affine de dimension 3. Nos arguments sont de nature variée, et s’appuient sur l’action du groupe modéré sur un complexe carréCAT(0) et Gromov hyperbolique récemment introduite par Bisi, Furter et Lamy.Nous avons finalement collecté dans un dernier et court chapitre quelques pistes de recherchedirectement inspirées des travaux présentés iciThis thesis is divided into three independent chapters on the iterates of rational maps on projective varieties and more specifically on the study of the growth of the degree sequences of the iterates of such maps. In the first chapter, we give a construction of the fundamental invariants called dynamical degrees. Our method holds in a very general setting, without any conditions on the characteristic of the field or on the singularities of the ambient space.This construction is based on the study of positivity properties of algebraic cycles and gives an alternative approach to the analytical technics of Dinh and Sibony or to the algebraic arguments of Truong.The second chapter is taken from an article written in joint work with Jian Xiao. Our paper focuses on central objects in convex geometry called valuations. We transfer some positivity notions of algebraic cycles recently introduced by Lehmann and Xiao, this allows us to extend the convolution operation defined by Bernig and Fu to a subspace of sufficiently positive valuations.The third chapter is the core of this thesis and focuses on the dynamical degrees of the so-called tame automorphisms of an affine quadric threefold. Our arguments are of various nature and rely on the action of the tame group on a CAT(0), Gromov hyperbolic square complex recently introduced by Bisi, Furter and Lamy. Finally, we have collected in the last chapter a few perpectives directly inspired by this work
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Evers, Dirk J. "RNA folding via algebraic dynamic programming." [S.l. : s.n.], 2003. http://deposit.ddb.de/cgi-bin/dokserv?idn=968564844.
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Itzá-Ortiz, Benjamín A. "The C*-algebras associated with irrational time homeomorphisms of suspensions /." view abstract or download file of text, 2003. http://wwwlib.umi.com/cr/uoregon/fullcit?p3095252.
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Thesis (Ph. D.)--University of Oregon, 2003.Typescript. Includes vita and abstract. Includes bibliographical references (leaves 68-69). Also available for download via the World Wide Web; free to University of Oregon users.
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Phillips, Caitlin. "An algebraic approach to dynamic epistemic logic." Thesis, McGill University, 2010. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=86767.
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In reasoning about multi-agent systems, it is important to look beyond the realm of propositional logic and to reason about the knowledge of agents within the system, as what they know about the environment will affect how they behave. A useful tool for formalizing and analyzing what agents know is epistemic logic, a modal logic developed by philosophers in the early 1960s. Epistemic logic is key to understanding knowledge in multi-agent systems, but insufficient if one wishes to study how the agents' knowledge changes over time. To do this, it is necessary to use a logic that combines dynamic and epistemic modalities, called dynamic epistemic logic. Some formalizations of dynamic epistemic logic use Kripke semantics for the states and actions, while others take a more algebraic approach, and use order-theoretic structures in their semantics. We discuss several of these logics, but focus predominantly on the algebraic framework for dynamic epistemic logic.Past approaches to dynamic epistemic logic have typically been focused on actions whose primary purpose is to communicate information from one agent to another. These actions are unable to alter the valuation of any proposition within the system. In fields such as security and economics, it is easy to imagine situations in which this sort of action would be insufficient. Instead, we expand the framework to include both communication actions and actions that change the state of the system. Furthermore, we propose a new modality which captures both epistemic and propositional changes that result from the agents' actions.
En raisonnement sur les systemes multi-agents, il est important de regarder au-dela du domaine de la logique propositionnelle et de raisonner sur les con- naissances des agents au sein du syst`eme, parce que ce qu'ils savent au sujet de l'environnement influe sur la mani`ere dont ils se comportent. Un outil utile pour l'analyse et la formalisation de ce que les agents savent, est la logique epistemique, une logique modale developpee par les philosophes du debut des annees 1960. La logique epistemique est la cle de la comprehension des connaissances dans les systemes multi-agents, mais elle est insuffisante si l'on veut etudier la facon dont la connaissance des agents evolue a travers le temps. Pour ce faire, il est necessaire de recourir a une logique qui allie des modalites dynamiques et epistemiques, appele la logique epistemique dynamique. Certaines formalisations de la logique epistemique dynamique utilisent la semantique de Kripke pour les etats et les actions, tandis que d'autres prennent une approche algebrique, et utilisent les structures ordonne dans leur semantique. Nous discutons plusieurs de ces logiques, mais nous nous concentrons principalement sur le cadre algebrique pour la logique epistemique dynamique.
Les approches adoptees dans le passe a la logique epistemique dynamique ont generalement ete axe sur les actions dont l'objectif principal est de communiquer des informations d'un agent a un autre. Ces actions sont dans l'impossibilite de modifier l' evaluation de toute proposition au sein du systeme. Dans des domaines tels que la securite et l' economie, il est facile d'imaginer des situations dans lesquelles ce type d'action serait insuffisante. Au lieu de cela, nous etendons le cadre algebrique pour inclure a la fois des actions de communication et des actions qui changent l' etat du systeme. En outre, nous proposons une nouvelle modalite qui permet de capturer a la fois les changements epistemiques et les changements propositionels qui resultent de l'action des agents.
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Maffeis, Sergio. "Dynamic Web data : a process algebraic approach." Thesis, Imperial College London, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.436321.
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Höner, zu Siederdissen Christian, Sonja J. Prohaska, and Peter F. Stadler. "Algebraic dynamic programming over general data structures." Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-206280.
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Background: Dynamic programming algorithms provide exact solutions to many problems in computational biology, such as sequence alignment, RNA folding, hidden Markov models (HMMs), and scoring of phylogenetic trees. Structurally analogous algorithms compute optimal solutions, evaluate score distributions, and perform stochastic sampling. This is explained in the theory of Algebraic Dynamic Programming (ADP) by a strict separation of state space traversal (usually represented by a context free grammar), scoring (encoded as an algebra), and choice rule. A key ingredient in this theory is the use of yield parsers that operate on the ordered input data structure, usually strings or ordered trees. The computation of ensemble properties, such as a posteriori probabilities of HMMs or partition functions in RNA folding, requires the combination of two distinct, but intimately related algorithms, known as the inside and the outside recursion. Only the inside recursions are covered by the classical ADP theory. Results: The ideas of ADP are generalized to a much wider scope of data structures by relaxing the concept of parsing. This allows us to formalize the conceptual complementarity of inside and outside variables in a natural way. We demonstrate that outside recursions are generically derivable from inside decomposition schemes. In addition to rephrasing the well-known algorithms for HMMs, pairwise sequence alignment, and RNA folding we show how the TSP and the shortest Hamiltonian path problem can be implemented efficiently in the extended ADP framework. As a showcase application we investigate the ancient evolution of HOX gene clusters in terms of shortest Hamiltonian paths. Conclusions: The generalized ADP framework presented here greatly facilitates the development and implementation of dynamic programming algorithms for a wide spectrum of applications.
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Epple, Alexander. "Methods for increased computational efficiency of multibody simulations." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/26532.
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Thesis (Ph. D.)--Aerospace Engineering, Georgia Institute of Technology, 2009.Committee Chair: Olivier A. Bauchau; Committee Member: Andrew Makeev; Committee Member: Carlo L. Bottasso; Committee Member: Dewey H. Hodges; Committee Member: Massimo Ruzzene. Part of the SMARTech Electronic Thesis and Dissertation Collection.
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Papathanasiou, Dimitrios. "Hypercyclic Algebras and Affine Dynamics." Bowling Green State University / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1490913276727982.
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Beersing-Vasquez, Kiran. "Suturing in Surgical Simulations." Thesis, KTH, Numerisk analys, NA, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-260254.
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The goal of this project is to develop virtual surgical simulation software in order to simulate the suturing and knot tying processes associated with surgical thread. State equations are formulated using Lagrangian mechanics, which is useful for the conservation of energy. Solver methods are developed with theory based in Differential Algebraic Equations (DAEs) which concern governing Ordinary Differential Equations (ODEs) that are constraint with Algebraic Equations (AE). An implicit integration scheme and Newton's method is used to solve the system in each step. Furthermore, a collision response process based on the Linear Complementarity Problem (LCP) is implemented to handle collisions and measure their forces. Models have been developed to represent the different types of objects. A spline model is used to represent the suture and mass-spring model for the tissue. They were both selected for their efficiency and base on real physical properties. The spline model was also chosen as it is continuous and can be evaluated at any point along the length. Other objects are also defined such as rigid bodies. The Lagrangian multiplier method is used to define the constraints in the model. This allows for the construction of complex models. An important constraint is the suturing constraint, which is created when a sufficient force is applied by the suture tip on to the tissue. This constraint allows only a sliding point along the suture to pass through a specific point on the tissue. This results in a virtual suturing model which can be built on for use in surgical simulations. Further investigations would be interesting to increase performance, accuracy and scope of the simulator.Det här projektet syftar till att utveckla mjukvara för virtuell simulering av kirurgi som involverar knytande av suturtråd. Lagranges ekvationer används för att härleda energibevarande tillståndsekvationer. Lösningsmetoderna grundar sig i teori från området Differential-Algebraiska Ekvationer (DAEer), som avser att kontrollera Ordinära Differentialekvationer (ODEer) med algebraiska bivillkor. Ett implicit integrationsschema och Newtons metod används för att lösa systemet i varje steg. Utöver det så implementeras en kollisionsrespons-process baserad på det linjära komplementaritetsproblemet (LCP) för att hantera kollisioner och mäta deras krafter. Modeller har utvecklats för att representera olika typer av objekt. En spline-modell används för att representera suturtråden och ett mass-fjäder system för vävnaden. Valet baserades på deras höga prestanda samt starka anknytning till objektens fysiska egenskaper. Spline-modellen valdes också då dess kontinuitet innebär att den går att evaluera för en godtycklig punkt inom dess domän. Andra objekt, såsom stela kroppar, finns också definierade. Lagrangemultiplikator används för att definiera bivillkor i modellen. Detta tillåter konstruktionen av komplexa modeller. Ett viktigt bivillkor är sutur-bivillkoret som uppstår när tillräcklig kraft från spetsen på den kirurgiska nålen appliceras på vävnaden. Detta bivillkor tillåter att endast en glidande punkt längsmed suturen passerar genom en specifik punkt på vävnaden. Detta resulterar i en virtuell modell för stygn som kan byggas vidare på för användning i kirurgiska simulationer. Det vore intressant med ytterligare undersökningar för att förbättra prestandan, precisionen och simulatorns omfattning.
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Nyqvist, Robert. "Algebraic Dynamical Systems, Analytical Results and Numerical Simulations." Doctoral thesis, Växjö : Växjö University Press, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-1142.
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Wang, Rui. "Distributed Cooperative Communications and Wireless Power Transfer." Digital WPI, 2018. https://digitalcommons.wpi.edu/etd-dissertations/62.
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In telecommunications, distributed cooperative communications refer to techniques which allow different users in a wireless network to share or combine their information in order to increase diversity gain or power gain. Unlike conventional point-to-point communications maximizing the performance of the individual link, distributed cooperative communications enable multiple users to collaborate with each other to achieve an overall improvement in performance, e.g., improved range and data rates.
The first part of this dissertation focuses the problem of jointly decoding binary messages from a single distant transmitter to a cooperative receive cluster. The outage probability of distributed reception with binary hard decision exchanges is compared with the outage probability of ideal receive beamforming with unquantized observation exchanges. Low- dimensional analysis and numerical results show, via two simple but surprisingly good approximations, that the outage probability performance of distributed reception with hard decision exchanges is well-predicted by the SNR of ideal receive beamforming after subtracting a hard decision penalty of slightly less than 2 dB. These results, developed in non-asymptotic regimes, are consistent with prior asymptotic results (for a large number of nodes and low per-node SNR) on hard decisions in binary communication systems.
We next consider the problem of estimating and tracking channels in a distributed transmission system with multiple transmitters and multiple receivers. In order to track and predict the effective channel between each transmit node and each receive node to facilitate coherent transmission, a linear time-invariant state- space model is developed and is shown to be observable but nonstabilizable. To quantify the steady-state performance of a Kalman filter channel tracker, two methods are developed to efficiently compute the steady-state prediction covariance. An asymptotic analysis is also presented for the homogenous oscillator case for systems with a large number of transmit and receive nodes with closed-form results for all of the elements in the asymptotic prediction covariance as a function of the carrier frequency, oscillator parameters, and channel measurement period. Numeric results confirm the analysis and demonstrate the effect of the oscillator parameters on the ability of the distributed transmission system to achieve coherent transmission.
In recent years, the development of efficient radio frequency (RF) radiation wireless power transfer (WPT) systems has become an active research area, motivated by the widespread use of low-power devices that can be charged wirelessly. In this dissertation, we next consider a time division multiple access scenario where a wireless access point transmits to a group of users which harvest the energy and then use this energy to transmit back to the access point. Past approaches have found the optimal time allocation to maximize sum throughput under the assumption that the users must use all of their harvested power in each block of the "harvest-then-transmit" protocol. This dissertation considers optimal time and energy allocation to maximize the sum throughput for the case when the nodes can save energy for later blocks. To maximize the sum throughput over a finite horizon, the initial optimization problem is separated into two sub-problems and finally can be formulated into a standard box- constrained optimization problem, which can be solved efficiently. A tight upper bound is derived by relaxing the energy harvesting causality.
A disadvantage of RF-radiation based WPT is that path loss effects can significantly reduce the amount of power received by energy harvesting devices. To overcome this problem, recent investigations have considered the use of distributed transmit beamforming (DTB) in wireless communication systems where two or more individual transmit nodes pool their antenna resources to emulate a virtual antenna array. In order to take the advantages of the DTB in the WPT, in this dissertation, we study the optimization of the feedback rate to maximize the energy efficiency in the WPT system. Since periodic feedback improves the beamforming gain but requires the receivers to expend energy, there is a fundamental tradeoff between the feedback period and the efficiency of the WPT system. We develop a new model to combine WPT and DTB and explicitly account for independent oscillator dynamics and the cost of feedback energy from the receive nodes. We then formulate a "Normalized Weighted Mean Energy Harvesting Rate" (NWMEHR) maximization problem to select the feedback period to maximize the weighted averaged amount of net energy harvested by the receive nodes per unit of time as a function of the oscillator parameters. We develop an explicit method to numerically calculate the globally optimal feedback period.
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Vassiliadis, Vassilios. "Computational solution of dynamic optimization problems with general differential-algebraic constraints." Thesis, Imperial College London, 1993. http://hdl.handle.net/10044/1/7567.
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Hanselmann, Thomas. "Approximate dynamic programming with adaptive critics and the algebraic perceptron as a fast neural network related to support vector machines." University of Western Australia. School of Electrical, Electronic and Computer Engineering, 2003. http://theses.library.uwa.edu.au/adt-WU2004.0005.
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[Truncated abstract. Please see the pdf version for the complete text. Also, formulae and special characters can only be approximated here. Please see the pdf version of this abstract for an accurate reproduction.] This thesis treats two aspects of intelligent control: The first part is about long-term optimization by approximating dynamic programming and in the second part a specific class of a fast neural network, related to support vector machines (SVMs), is considered. The first part relates to approximate dynamic programming, especially in the framework of adaptive critic designs (ACDs). Dynamic programming can be used to find an optimal decision or control policy over a long-term period. However, in practice it is difficult, and often impossible, to calculate a dynamic programming solution, due to the 'curse of dimensionality'. The adaptive critic design framework addresses this issue and tries to find a good solution by approximating the dynamic programming process for a stationary environment. In an adaptive critic design there are three modules, the plant or environment to be controlled, a critic to estimate the long-term cost and an action or controller module to produce the decision or control strategy. Even though there have been many publications on the subject over the past two decades, there are some points that have had less attention. While most of the publications address the training of the critic, one of the points that has not received systematic attention is training of the action module.¹ Normally, training starts with an arbitrary, hopefully stable, decision policy and its long-term cost is then estimated by the critic. Often the critic is a neural network that has to be trained, using a temporal difference and Bellman's principle of optimality. Once the critic network has converged, a policy improvement step is carried out by gradient descent to adjust the parameters of the controller network. Then the critic is retrained again to give the new long-term cost estimate. However, it would be preferable to focus more on extremal policies earlier in the training. Therefore, the Calculus of Variations is investigated to discard the idea of using the Euler equations to train the actor. However, an adaptive critic formulation for a continuous plant with a short-term cost as an integral cost density is made and the chain rule is applied to calculate the total derivative of the short-term cost with respect to the actor weights. This is different from the discrete systems, usually used in adaptive critics, which are used in conjunction with total ordered derivatives. This idea is then extended to second order derivatives such that Newton's method can be applied to speed up convergence. Based on this, an almost concurrent actor and critic training was proposed. The equations are developed for any non-linear system and short-term cost density function and these were tested on a linear quadratic regulator (LQR) setup. With this approach the solution to the actor and critic weights can be achieved in only a few actor-critic training cycles. Some other, more minor issues, in the adaptive critic framework are investigated, such as the influence of the discounting factor in the Bellman equation on total ordered derivatives, the target interpretation in backpropagation through time as moving and fixed targets, the relation between simultaneous recurrent networks and dynamic programming is stated and a reinterpretation of the recurrent generalized multilayer perceptron (GMLP) as a recurrent generalized finite impulse MLP (GFIR-MLP) is made. Another subject in this area that is investigated, is that of a hybrid dynamical system, characterized as a continuous plant and a set of basic feedback controllers, which are used to control the plant by finding a switching sequence to select one basic controller at a time. The special but important case is considered when the plant is linear but with some uncertainty in the state space and in the observation vector, and a quadratic cost function. This is a form of robust control, where a dynamic programming solution has to be calculated. ¹Werbos comments that most treatment of action nets or policies either assume enumerative maximization, which is good only for small problems, except for the games of Backgammon or Go [1], or, gradient-based training. The latter is prone to difficulties with local minima due to the non-convex nature of the cost-to-go function. With incremental methods, such as backpropagation through time, calculus of variations and model-predictive control, the dangers of non-convexity of the cost-to-go function with respect to the control is much less than the with respect to the critic parameters, when the sampling times are small. Therefore, getting the critic right has priority. But with larger sampling times, when the control represents a more complex plan, non-convexity becomes more serious.
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Hays, Joseph T. "Parametric Optimal Design Of Uncertain Dynamical Systems." Diss., Virginia Tech, 2011. http://hdl.handle.net/10919/28850.
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This research effort develops a comprehensive computational framework to support the parametric optimal design of uncertain dynamical systems. Uncertainty comes from various sources, such as: system parameters, initial conditions, sensor and actuator noise, and external forcing. Treatment of uncertainty in design is of paramount practical importance because all real-life systems are affected by it; not accounting for uncertainty may result in poor robustness, sub-optimal performance and higher manufacturing costs.
Contemporary methods for the quantification of uncertainty in dynamical systems are computationally intensive which, so far, have made a robust design optimization methodology prohibitive. Some existing algorithms address uncertainty in sensors and actuators during an optimal design; however, a comprehensive design framework that can treat all kinds of uncertainty with diverse distribution characteristics in a unified way is currently unavailable. The computational framework uses Generalized Polynomial Chaos methodology to quantify the effects of various sources of uncertainty found in dynamical systems; a Least-Squares Collocation Method is used to solve the corresponding uncertain differential equations. This technique is significantly faster computationally than traditional sampling methods and makes the construction of a parametric optimal design framework for uncertain systems feasible.
The novel framework allows to directly treat uncertainty in the parametric optimal design process. Specifically, the following design problems are addressed: motion planning of fully-actuated and under-actuated systems; multi-objective robust design optimization; and optimal uncertainty apportionment concurrently with robust design optimization. The framework
advances the state-of-the-art and enables engineers to produce more robust and optimally performing designs at an optimal manufacturing cost.Ph. D.
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Dagli, Mehmet. "Lie algebra decompositions with applications to quantum dynamics." [Ames, Iowa : Iowa State University], 2008.
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Frazier, William. "Application of Symplectic Integration on a Dynamical System." Digital Commons @ East Tennessee State University, 2017. https://dc.etsu.edu/etd/3213.
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Molecular Dynamics (MD) is the numerical simulation of a large system of interacting molecules, and one of the key components of a MD simulation is the numerical estimation of the solutions to a system of nonlinear differential equations. Such systems are very sensitive to discretization and round-off error, and correspondingly, standard techniques such as Runge-Kutta methods can lead to poor results. However, MD systems are conservative, which means that we can use Hamiltonian mechanics and symplectic transformations (also known as canonical transformations) in analyzing and approximating solutions. This is standard in MD applications, leading to numerical techniques known as symplectic integrators, and often, these techniques are developed for well-understood Hamiltonian systems such as Hill’s lunar equation. In this presentation, we explore how well symplectic techniques developed for well-understood systems (specifically, Hill’s Lunar equation) address discretization errors in MD systems which fail for one or more reasons.
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Miles, Richard Craig. "Arithmetic dynamical systems." Thesis, University of East Anglia, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.323222.
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Hinkelmann, Franziska Babette. "Algebraic theory for discrete models in systems biology." Diss., Virginia Tech, 2011. http://hdl.handle.net/10919/28509.
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This dissertation develops algebraic theory for discrete models in systems biology. Many discrete model types can be translated into the framework of polynomial dynamical systems (PDS), that is, time- and state-discrete dynamical systems over a finite field where the transition function for each variable is given as a polynomial. This allows for using a range of theoretical and computational tools from computer algebra, which results in a powerful computational engine for model construction, parameter estimation, and analysis methods. Formal definitions and theorems for PDS and the concept of PDS as models of biological systems are introduced in section 1.3.
Constructing a model for given time-course data is a challenging problem. Several methods for reverse-engineering, the process of inferring a model solely based on experimental data, are described briefly in section 1.3. If the underlying dependencies of the model components are known in addition to experimental data, inferring a "good" model amounts to parameter estimation.
Chapter 2 describes a parameter estimation algorithm that infers a special class of polynomials, so called nested canalyzing functions. Models consisting of nested canalyzing functions have been shown to exhibit desirable biological properties, namely robustness and stability. The algorithm is based on the parametrization of nested canalyzing functions. To demonstrate the feasibility of the method, it is applied to the cell-cycle network of budding yeast.
Several discrete model types, such as Boolean networks, logical models, and bounded Petri nets, can be translated into the framework of PDS. Section 3 describes how to translate agent-based models into polynomial dynamical systems.
Chapter 4, 5, and 6 are concerned with analysis of complex models. Section 4 proposes a new method to identify steady states and limit cycles. The method relies on the fact that attractors correspond to the solutions of a system of polynomials over a finite field, a long-studied problem in algebraic geometry which can be efficiently solved by computing Gröbner bases. Section 5 introduces a bit-wise implementation of a Gröbner basis algorithm for Boolean polynomials. This implementation has been incorporated into the core engine of Macaulay2. Chapter 6 discusses bistability for Boolean models formulated as polynomial dynamical systems.Ph. D.
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at, Andreas Cap@esi ac. "Graded Lie Algebras and Dynamical Systems." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi1086.ps.
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Nakano, Anderson Luis. "Superfícies de pontos dinâmicas." Universidade de São Paulo, 2009. http://www.teses.usp.br/teses/disponiveis/55/55134/tde-06052009-144752/.
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O estudo do comportamento de fluidos é um antigo domínio das ciências da natureza. Ultimamente, fenômenos de engenharia que eram estudados empiricamente passaram a ser estudados com auxílio computacional. A Dinâmica de Fluidos Computacional (DFC) é a área da ciência da computação que estuda métodos computacionais para simulação de escoamento de fluidos, e muitas vezes é a forma mais prática, ou a única, de se observar fenômenos de interesse no escoamento. Este projeto de Mestrado procurou investigar, no âmbito da simulação de um escoamento bifásico, métodos computacionais para representar a interface entre dois fluidos imiscíveis. A separação dos fluidos por meio de uma interface é necessária para assegurar que, propriedades como viscosidade e densidade, específicas de cada fluido, sejam utilizadas corretamente para o cálculo do movimento de seus respectivos fluidos. Desenvolvemos um método lagrangeano sem a utilização de malhas com o objetivo de suprir algumas restrições de trabalhos prévios. Para representar a interface entre os dois fluidos, este método utiliza uma técnica de reconstrução de superfícies baseada em aproximações de superfícies algébricas de alta ordem. Os resultados numéricos reportados neste documento evidenciam o potencial da nossa abordagemThe study of the behaviour of fluids is an ancient field in natural sciences. Recently, engineering phenomena that were empirically studied started to be done with computacional aid. The Computational Fluid Dynamics (CFD) is the area of science that studies computational methods for computer simulation of fluid flow, and often is the most practical way, or the only, to observe phenomena of interest in flow. This Masters degree project sought to investigate, in the context of the simulation of biphasic flows, computational methods to represent the interface between two immiscible fluids. The separation of fluids by the means of an interface is required to ensure that, during the simulation, the physical properties of a fluid, like density and viscosity (specific of each fluid) are properly used in the calculus of the respective fluid motion. We developed a lagrangean method without the use of mesh with the goal of alleviating some of the previous works restrictions. To represent the interface between the two fluids, this method uses a surface reconstruction technique based on approximations of high order algebraic surfaces. The numerical results reported herein show the potential of our approach
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Le, Van Tu. "Dynamique des endomorphismes post-critiquement algébriques." Thesis, Toulouse 3, 2020. http://www.theses.fr/2020TOU30151.
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Dans cette thèse, j'étudie la dynamique des endomorphismes de l'espace projectif complexe. Je m'intéresse aux endomorphismes post-critiquement algébriques, une notion qui généralise celle de fractions rationnelles post-critiquement finies en dimension 1. En particulier, j'étudie les valeurs propres d'un endomorphisme post-critiquement algébrique le long de l'orbite d'un point périodique. En dimension 1, un résultat bien connu, qui remonte aux travaux de Pierre Fatou, dit que ces valeurs sont soit nulles soit de module strictement plus supérieur à 1. Dans cette thèse, j'étudie une conjecture qui généralise ce résultat en dimension au moins 2. Dans la première partie de cette thèse, j'étudie une famille des endomorphismes post-critiquement algébriques introduite dans la thèse de Sarah Koch. En utilisant la caractérisation topologique des fractions rationnelles de William Thurston, sous certaines conditions, Sarah Koch a associé à une fraction rationnelle post-critiquement finie g un endomorphisme post-critiquement algébrique f. Lorsque g est un polynôme quadratique, je donne une caractérisation détaillée des valeurs propres de l'endomorphisme associé f en ses points fixes. En particulier, je montre que celles-ci sont soit nulles soit de modules strictement supérieurs à 1. Ce résultat suggère la validité de la conjecture. Dans la deuxième partie, je montre que la conjecture est vraie dans le cas de dimension 2 sans hypothèse supplémentaire et en toute dimension lorsque les points périodiques sont en dehors de l'ensemble post-critique et sans autre hypothèseIn this thesis, I study the dynamics of endomorphisms of the complex projective space. I am interested in post-critically algebraic endomorphisms, a notion which generalizes that of post-critically finite rational maps in dimension 1. In particular, I study the eigenvalues of a post-critically algebraic endomorphism along the orbit of a periodic point. In dimension 1, a well-known result, which is due to Pierre Fatou, states that these values are either zero or of modules strictly greater than 1. In this thesis, I study a conjecture which generalizes this result in dimension at least 2. In the first part of this thesis, I study a family of post-critically algebraic endo- morphisms introduced in Sarah Koch's thesis. Using the topological characterization of rational maps of William Thurston, under certain conditions, Sarah Koch associated with a post-critically finite rational map g a post-critically algebraic endomorphism f. When g is a quadratic polynomial, I give a detailed characterization of the eigenvalues of the endomorphism f at its fixed points. In particular, I show that these values are either zero or of modules strictly greater than 1. This result provides evidence of the validity of the conjecture. In the second part, I show that the conjecture is true in the case of dimension 2 without additional hypotheses and in any dimension when the periodic points are outside the post-critical set and without other hypotheses
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Song, Xuefeng. "Dynamic modeling issues for power system applications." Texas A&M University, 2003. http://hdl.handle.net/1969.1/1591.
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Power system dynamics are commonly modeled by parameter dependent nonlinear differential-algebraic equations (DAE) x p y x f ) and 0 = p y x g ) . Due to
(,, (,, the algebraic constraints, we cannot directly perform integration based on the DAE. Traditionally, we use implicit function theorem to solve for fast variables y to get a reduced model in terms of slow dynamics locally around x or we compute y numerically at each x . However, it is well known that solving nonlinear algebraic equations analytically is quite difficult and numerical solution methods also face many uncertainties since nonlinear algebraic equations may have many solutions, especially around bifurcation points. In this thesis, we apply the singular perturbation method to model power system dynamics in a singularly perturbed ODE (ordinary-differential equation) form, which makes it easier to observe time responses and trace bifurcations without reduction process. The requirements of introducing the fast dynamics are investigated and the complexities in the procedures are explored. Finally, we propose PTE (Perturb and Taylors expansion) technique to carry out our goal to convert a DAE to an explicit state space form of ODE. A simplified unreduced Jacobian matrix is also introduced. A dynamic voltage stability case shows that the proposed method works well without complicating the applications.
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Parra, Rodrigo. "Equidistribution towards the Green current in complex dynamics." Doctoral thesis, KTH, Matematik (Inst.), 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-34264.
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Given a holomorphic self-map of complex projective space of de-gree larger than one, we prove that there exists a finite collection oftotally invariant algebraic sets with the following property: given anypositive closed (1,1)-current of mass 1 with no mass on any element of this family, the sequence of normalized pull-backs of the current converges to the Green current. Under suitable geometric conditions on the collection of totally invariant algebraic sets, we prove a sharper equidistribution result.QC 20110530
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Sayer, Ryan Thomas. "Quantum Dynamics Using Lie Algebras, with Explorations in the Chaotic Behavior of Oscillators." BYU ScholarsArchive, 2012. https://scholarsarchive.byu.edu/etd/3285.
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We study the time evolution of driven quantum systems using analytic, algebraic, and numerical methods. First, we obtain analytic solutions for driven free and oscillator systems by shifting the coordinate and phase of the undriven wave function. We also factorize the quantum evolution operator using the generators of the Lie algebra comprising the Hamiltonian. We obtain coupled ODE's for the time evolution of the Lie algebra parameters. These parameters allow us to find physical properties of oscillator dynamics. In particular we find phase-space trajectories and transition probabilities. We then search for chaotic behavior in the Lie algebra parameters as a signature for dynamical chaos in the quantum system. We plot the trajectories, transition probabilities, and Lyapunov exponents for a wide range of the following physical parameters: strength and duration of the driving force, frequency difference, and anharmonicity of the oscillator. We identify conditions for the appearance of chaos in the system.
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Adiguzel, Mehmet Emin. "A new control treatise of dynamic systems via algebraic state equations "Direct Optimal Control" /." The Ohio State University, 1994. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487858417983374.
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Svensson, Carl-Magnus. "Dynamics of spatially extended dendrites." Thesis, University of Nottingham, 2009. http://eprints.nottingham.ac.uk/10788/.
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Dendrites are the most visually striking parts of neurons. Even so many neuron models are of point type and have no representation of space. In this thesis we will look at a range of neuronal models with the common property that we always include spatially extended dendrites. First we generalise Abbott’s “sum-over-trips” framework to include resonant currents. We also look at piece-wise linear (PWL) models and extend them to incorporate spatial structure in the form of dendrites. We look at the analytical construction of orbits for PWL models. By using both analytical and numerical Lyapunov exponent methods we explore phase space and in particular we look at mode-locked solutions. We will then construct the phase response curve (PRC) for a PWL system with compartmentally modelled dendrites. This sets us up so we can look at the effect of multiple PWL systems that are weakly coupled through gap junctions. We also attach a continuous dendrite to a PWL soma and investigate how the position of the gap junction influences network properties. After this we will present a short overview of neuronal plasticity with a special focus on the spatial effects. We also discuss attenuation of distal synaptic input and how this can be countered by dendritic democracy as this will become an integral part of our learning mechanisms. We will examine a number of different learning approaches including the tempotron and spike-time dependent plasticity. Here we will consider Poisson’s equation around a neural membrane. The membrane we focus on has Hodgkin-Huxley dynamics so we can study action potential propagation on the membrane. We present the Green’s function for the case of a one-dimensional membrane in a two-dimensional space. This will allow us to examine the action potential initiation and propagation in a multi-dimensional axon.
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Cirstea, Corina. "Integrating observations and computations in the specification of state-based, dynamical systems." Thesis, University of Oxford, 2000. https://eprints.soton.ac.uk/263009/.
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The overall goal of this work is to combine the complementary contributions of algebra and coalgebra to specification, in order to provide a formal framework for the specification of state-based, dynamical systems. Algebraic specification methods benefit from the availability of inductive techniques for defining and reasoning about structures that involve computation; coalgebraic specification methods complement algebraic ones both in their objectives and in their means of achieving them, by employing coinductive techniques for defining and reasoning about structures that involve observation. State-based, dynamical systems comprise a computational aspect, concerned with the construction of (new) system states, and an observational aspect, concerned with the observation of (existing) system states, with the two aspects overlapping on features concerned with the evolution of system states. Existing formalisms for the specification of such systems typically exploit the overlap between computational and observational features to employ either algebraic or coalgebraic techniques for specification and reasoning. However, such a choice limits the expressiveness of these formalisms w.r.t. either observational or computational features. Furthermore, the accounts given by such approaches to the concepts of indistinguishability by observations and respectively of reachability under computations are somewhat artificial, due to the failure to distinguish between computational and observational features. The approach taken here is to clearly separate the two categories of features (by shifting the features concerned with the evolution of system states to the computational component), and to use algebra and respectively coalgebra in formalising them. In particular, such an approach yields a coalgebraically-defined notion of indistinguishability by observations, and an algebraically-defined notion of reachability under computations. The relationship between computing new states and observing the resulting states is specified by suitably lifting the coalgebraic structure of the semantic domains induced by the observational component to computations over these semantic domains. Such an approach automatically results in a compatibility between computational and observational features, with the observational indistinguishability of states being preserved by computations, and with the reachability of states under computations being preserved by observations. Correctness properties of system behaviour are formalised using equational sentences. This is a standard technique in algebraic specification. A similar technique is used here for coalgebraic specification, with the resulting notion of sentence capturing system invariants quantified over state spaces. Moreover, a sound and complete calculus for reasoning about the specified behaviours is formulated in a concrete setting obtained by syntactically dualising the setting of many-sorted algebra. Equational sentences are then used to formalise the equivalence of computations as well as various system invariants, with the associated notions of satisfaction abstracting away observationally indistinguishable and respectively unreachable states, and with the associated proof techniques employing coinduction and respectively induction. Suitably instantiating the resulting approach yields a formalism for the specification and verification of objects.
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Gritsis, Dimitrios. "The dynamic simulation and optimal control of systems described by index two differential-algebraic equations." Thesis, Imperial College London, 1990. http://hdl.handle.net/10044/1/8535.
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Crumey, A. D. W. B. "Integrable dynamical systems associated with Kac-Moody algebras." Thesis, Imperial College London, 1988. http://hdl.handle.net/10044/1/47012.
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Filali, Amine Ghali. "Dynamical reflection algebras and associated boundary integrable models." Thesis, Cergy-Pontoise, 2011. http://www.theses.fr/2011CERG0567/document.
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Cette thèse s’inscrit dans le cadre général de la théorie des systèmes intégrables avec bords et le développement des structures algébriques associées.D’une part, nous nous attaquons au problème de la diagonalisation de l’hamiltonien du modèle XXZ avec bords non diagonaux. Nous exhibons les deux ensembles d’états propres et valeurs propres du modèle si les paramètres de bords satisfont deux conditions.D’autre part, nous introduisons un modèle de physique statistique que nous appelons le modèle face avec un bord réfléchissant. Nous calculons exactement sa fonction de partition et nous montrons que cette dernière se représente simplement sous la forme d’un unique déterminant matriciel.Nous montrons que ces deux problèmes sont reliés par la transformation vertex-face et exhibent une structure algébrique commune, l’algèbre de réflexion dynamique. Nous nous intéressons aux aspects mathématiques de cette algèbre dans le cas elliptique général,et nous introduisons deux classes de ces représentations, la représentation de co-module d’évaluation et sa duale. Nous pensons que cette algèbre est la structure clef pour l’analyse des modèles faces avec bords. En particulier, nous montrons à l’aide de twists de Drinfel’d que leur fonction de partition se représente simplement dans le cas général. Enfin, nous tentons une ’dynamisation’ du modèle à vertex ’Half-Turn-Symmetric’,et nous décrivons sa fonction de partition en termes de représentation d’évaluation de l’algèbre de Yang-Baxter dynamique, et trouvons un ensemble de conditions la déterminantunivoquementThis thesis is embedded in the general theory of quantum integrable models withboundaries, and the development of associated algebraic structures.We first consider the question of the diagonalization of the XXZ hamiltonian with nondiagonalboundaries. We succeed to find the two sets of eigenstates and eigenvalues of themodel if the boundaries parameters satisfy two conditions.We introduce then a statistical physics model which we refer to be the face model witha reflecting end. Moreover, we compute exactly its partition function and show that it takesthe form of a simple single matrix determinant.We show that these two problems are related through the vertex-face transformationand are solved using a common algebraic structure, the dynamical reflection algebra andits dual. We focus from a mathematical perspective on this algebra in the general ellipticcase. Both the co-module evaluation representation and its dual are introduced. We believethat these structures are the key ingredients for the analysis of face models with boundaries.In particular, using the concept of Drinfel’d twists, we show that the partition function ofthese models has a simple representation in the general case.Finally, we attempt on a ’dynamization’ of the Half-Turn-Symmetric vertexmodel. Wedescribe its partition function in terms of the evaluation representation of the dynamicalYang-Baxter algebra, and find a set of conditions that uniquely determine it
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Wang, Xuyan. "Landscape dynamic modelling with vector map algebra in GIS /." [St. Lucia, Qld.], 2004. http://www.library.uq.edu.au/pdfserve.php?image=thesisabs/absthe18161.pdf.
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Stigler, Brandilyn Suzanne. "An Algebraic Approach to Reverse Engineering with an Application to Biochemical Networks." Diss., Virginia Tech, 2005. http://hdl.handle.net/10919/28791.
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One goal of systems biology is to predict and modify the behavior of biological networks by accurately monitoring and modeling their responses to certain types of perturbations. The construction of mathematical models based on observation of these responses, referred to as reverse engineering, is an important step in elucidating the structure and dynamics of such networks. Continuous models, described by systems of differential equations, have been used to reverse engineer biochemical networks. Of increasing interest is the use of discrete models, which may provide a conceptual description of the network.
In this dissertation we introduce a discrete modeling approach, rooted in computational algebra, to reverse-engineer networks from experimental time series data. The algebraic method uses algorithmic tools, including Groebner-basis techniques, to build the set of all discrete models that fit time series data and to select minimal models from this set. The models used in this work are discrete-time finite dynamical systems, which, when defined over a finite field, are described by systems of polynomial functions. We present novel reverse-engineering algorithms for discrete models, where each algorithm is suitable for different amounts and types of data. We demonstrate the effectiveness of the algorithms on simulated networks and conclude with a description of an ongoing project to reverse-engineer a real gene regulatory network in yeast.Ph. D.
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Lacoursière, Claude. "Ghosts and machines : regularized variational methods for interactive simulations of multibodies with dry frictional contacts." Doctoral thesis, Umeå University, Computing Science, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-1143.
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A time-discrete formulation of the variational principle of mechanics is used to provide a consistent theoretical framework for the construction and analysis of low order integration methods. These are applied to mechanical systems subject to mixed constraints and dry frictional contacts and impacts---machines. The framework includes physics motivated constraint regularization and stabilization schemes. This is done by adding potential energy and Rayleigh dissipation terms in the Lagrangian formulation used throughout. These terms explicitly depend on the value of the Lagrange multipliers enforcing constraints. Having finite energy, the multipliers are thus massless ghost particles. The main numerical stepping method produced with the framework is called SPOOK.
Variational integrators preserve physical invariants globally, exactly in some cases, approximately but within fixed global bounds for others. This allows to product realistic physical trajectories even with the low order methods. These are needed in the solution of nonsmooth problems such as dry frictional contacts and in addition, they are computationally inexpensive. The combination of strong stability, low order, and the global preservation of invariants allows for large integration time steps, but without loosing accuracy on the important and visible physical quantities. SPOOK is thus well-suited for interactive simulations, such as those commonly used in virtual environment applications, because it is fast, stable, and faithful to the physics.
New results include a stable discretization of highly oscillatory terms of constraint regularization; a linearly stable constraint stabilization scheme based on ghost potential and Rayleigh dissipation terms; a single-step, strictly dissipative, approximate impact model; a quasi-linear complementarity formulation of dry friction that is isotropic and solvable for any nonnegative value of friction coefficients; an analysis of a splitting scheme to solve frictional contact complementarity problems; a stable, quaternion-based rigid body stepping scheme and a stable linear approximation thereof. SPOOK includes all these elements. It is linearly implicit and linearly stable, it requires the solution of either one linear system of equations of one mixed linear complementarity problem per regular time step, and two of the same when an impact condition is detected. The changes in energy caused by constraints, impacts, and dry friction, are all shown to be strictly dissipative in comparison with the free system. Since all regularization and stabilization parameters are introduced in the physics, they map directly onto physical properties and thus allow modeling of a variety of phenomena, such as constraint compliance, for instance.
Tutorial material is included for continuous and discrete-time analytic mechanics, quaternion algebra, complementarity problems, rigid body dynamics, constraint kinematics, and special topics in numerical linear algebra needed in the solution of the stepping equations of SPOOK.
The qualitative and quantitative aspects of SPOOK are demonstrated by comparison with a variety of standard techniques on well known test cases which are analyzed in details. SPOOK compares favorably for all these examples. In particular, it handles ill-posed and degenerate problems seamlessly and systematically. An implementation suitable for large scale performance and accuracy testing is left for future work.
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Hart, Robert. "A Non-commutative *-algebra of Borel Functions." Thèse, Université d'Ottawa / University of Ottawa, 2012. http://hdl.handle.net/10393/23235.
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To the pair (E,c), where E is a countable Borel equivalence relation on a standard Borel space (X,A) and c a normalized Borel T-valued 2-cocycle on E, we associate a sequentially weakly closed Borel *-algebra Br*(E,c), contained in the bounded linear operators on L^2(E). Associated to Br*(E,c) is a natural (Borel) Cartan subalgebra (Definition 6.4.10) L(Bo(X)) isomorphic to the bounded Borel functions on X. Then L(Bo(X)) and its normalizer (the set of the unitaries u in Br*(E,c) such that u*fu in L(Bo(X)), f in L(Bo(X))) countably generates the Borel *-algebra Br*(E,c). In this thesis, we study Br*(E,c) and in particular prove that: i) If E is smooth, then Br*(E,c) is a type I Borel *-algebra (Definition 6.3.10). ii) If E is a hyperfinite, then Br*(E,c) is a Borel AF-algebra (Definition 7.5.1). iii) Generalizing Kumjian's definition, we define a Borel twist G over E and its associated sequentially closed Borel *-algebra Br*(G). iv) Let a Borel Cartan pair (B, Bo) denote a sequentially closed Borel *-algebra B with a Borel Cartan subalgebra Bo, where B is countably Bo-generated. Generalizing Feldman-Moore's result, we prove that any pair (B, Bo) can be realized uniquely as a pair (Br*(E,c), L(Bo(X))). Moreover, we show that the pair (Br*(E,c), L(Bo(X))) is a complete invariant of the countable Borel equivalence relation E. v) We prove a Krieger type theorem, by showing that two aperiodic hyperfinite countable equivalence relations are isomorphic if and only if their associated Borel *-algebras Br*(E1) and Br*(E2) are isomorphic.
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Skjellum, Anthony Morari Manfred. "Concurrent dynamic simulation : multicomputer algorithms research applied to ordinary differential-algebraic process systems in chemical engineering /." Diss., Pasadena, Calif. : California Institute of Technology, 1990. http://resolver.caltech.edu/CaltechETD:etd-11132007-090727.
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Gatica, Ricardo A. "A binary dynamic programming problem with affine transitions and reward functions : properties and algorithm." Diss., Georgia Institute of Technology, 2002. http://hdl.handle.net/1853/32839.
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Seffrin, André [Verfasser]. "A Process-Algebraic Approach to Security-Aware Scheduling of Dynamic Partial Reconfiguration on FPGA Devices / André Seffrin." München : Verlag Dr. Hut, 2012. http://d-nb.info/1029399301/34.
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