Dissertations / Theses on the topic 'Combinatorial dynamical systems'
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Forrest, Alan Hunter. "Recurrence in dynamical systems : a combinatorial approach /." The Ohio State University, 1990. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487682558446011.
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Tiozzo, Giulio. "Entropy, Dimension and Combinatorial Moduli for One-Dimensional Dynamical Systems." Thesis, Harvard University, 2013. http://dissertations.umi.com/gsas.harvard:10891.
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The goal of this thesis is to provide a unified framework in which to analyze the dynamics of two seemingly unrelated families of one-dimensional dynamical systems, namely the family of quadratic polynomials and continued fractions. We develop a combinatorial calculus to describe the bifurcation set of both families and prove they are isomorphic. As a corollary, we establish a series of results describing the behavior of entropy as a function of the parameter. One of the most important applications is the relation between the topological entropy of quadratic polynomials and the Hausdorff dimension of sets of external rays landing on principal veins of the Mandelbrot set.Mathematics
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Ziegler, Caleb. "On Factors of Rank One Subshifts." Thesis, University of North Texas, 2018. https://digital.library.unt.edu/ark:/67531/metadc1157623/.
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Rank one subshifts are dynamical systems generated by a regular combinatorial process based on sequences of positive integers called the cut and spacer parameters. Despite the simple process that generates them, rank one subshifts comprise a generic set and are the source of many counterexamples. As a result, measure theoretic rank one subshifts, called rank one transformations, have been extensively studied and investigations into rank one subshifts been the basis of much recent work. We will answer several open problems about rank one subshifts. We completely classify the maximal equicontinuous factor for rank one subshifts, so that this factor can be computed from the parameters. We use these methods to classify when large classes of rank one subshifts have mixing properties. Also, we completely classify the situation when a rank one subshift can be a factor of another rank one subshift.
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Rothlisberger, Matthew Samuel. "Ergodic and Combinatorial Proofs of van der Waerden's Theorem." Scholarship @ Claremont, 2010. http://scholarship.claremont.edu/cmc_theses/14.
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Followed two different proofs of van der Waerden's theorem. Found that the two proofs yield important information about arithmetic progressions and the theorem. van der Waerden's theorem explains the occurrence of arithmetic progressions which can be used to explain such things as the Bible Code.
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Tastan, Mesut. "Analysis And Prediction Of Gene Expression Patterns By Dynamical Systems, And By A Combinatorial Algorithm." Master's thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/12606672/index.pdf.
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Modeling and prediction of gene-expression patterns has an important place in computational biology and bioinformatics. The measure of gene expression is determined from the genomic analysis at the mRNA level by means of microarray
technologies. Thus, mRNA analysis informs us not only about genetic viewpoints of an organism but also about the dynamic changes in environment of that organism. Different mathematical methods have been developed for analyzing
experimental data. In this study, we discuss the modeling approaches and the reasons why we concentrate on models derived from differential equations and improve the pioneering works in this field by including affine terms on the right-hand side of the nonlinear differential equations and by using Runge-
Kutta instead of Euler discretization, especially, with Heun&rsquos method. Herewith, for stability analysis we apply modified Brayton and Tong algorithm to time-discrete dynamics in an extended space.
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Paskauskas, Rytis. "Chaotic Scattering in Rydberg Atoms, Trapping in Molecules." Diss., Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/19809.
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We investigate chaotic ionization of highly excited hydrogen atom in crossed electric and magnetic fields (Rydberg atom) and intra-molecular relaxation in planar carbonyl sulfide (OCS) molecule. The underlying theoretical framework of our studies is dynamical systems theory and periodic orbit theory. These theories offer formulae to compute expectation values of observables in chaotic systems with best accuracy available in given circumstances, however they require to have a good control and reliable numerical tools to compute unstable periodic orbits. We have developed such methods of computation and partitioning of the phase space of hydrogen atom in crossed at right angles electric and magnetic fields, represented by a two degree of freedom (dof) Hamiltonian system. We discuss extensions to a 3-dof setting by developing the methodology to compute unstable invariant tori, and applying it to the planar OCS, represented by a 3-dof Hamiltonian. We find such tori important in explaining anomalous relaxation rates in chemical reactions. Their potential application in Transition State Theory is discussed.
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Lan, Yueheng. "Dynamical systems approach to one-dimensional spatiotemporal chaos -- A cyclist's view." Diss., Available online, Georgia Institute of Technology, 2004:, 2004. http://etd.gatech.edu/theses/available/etd-10282004-154606/unrestricted/lan%5Fyueheng%5F200412%5Fphd.pdf.
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Thesis (Ph. D.)--Physics, Georgia Institute of Technology, 2005.Jean Bellissard, Committee Member ; Turgay Uzer, Committee Member ; Roman Grigoriev, Committee Member ; Konstantin Mischaikow, Committee Member ; Predrag Cvitanovic, Committee Chair. Vita. Includes bibliographical references.
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Demaeyer, Jonathan. "Escape rate theory for noisy dynamical systems." Doctoral thesis, Universite Libre de Bruxelles, 2013. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209440.
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The escape of trajectories is a ubiquitous phenomenon in open dynamical systems and stochastic processes. If escape occurs repetitively for a statistical ensemble of trajectories, the population of remaining trajectories often undergoes an exponential decay characterised by the so-called escape rate. Its inverse defines the lifetime of the decaying state, which represents an intrinsic property of the system. This paradigm is fundamental to nucleation theory and reaction-rate theory in chemistry, physics, and biology.In many circumstances, escape is activated by the presence of noise, which may be of internal or external origin. This is the case for thermally activated escape over a potential energy barrier and, more generally, for noise-induced escape in continuous-time or discrete-time dynamics.
In the weak-noise limit, the escape rate is often observed to decrease exponentially with the inverse of the noise amplitude, a behaviour which is given by the van't Hoff-Arrhenius law of chemical kinetics. In particular, the two important quantities to determine in this case are the exponential dependence (the ``activation energy') and its prefactor.
The purpose of the present thesis is to develop an analytical method to determine these two quantities. We consider in particular one-dimensional continuous and discrete-time systems perturbed by Gaussian white noise and we focus on the escape from the basin of attraction of an attracting fixed point.
In both classes of systems, using path-integral methods, a formula is deduced for the noise-induced escape rate from the attracting fixed point across an unstable fixed point, which forms the boundary of the basin of attraction. The calculation starts from the trace formula for the eigenvalues of the operator ruling the time evolution of the probability density in noisy maps. The escape rate is determined by the loop formed by two heteroclinic orbits connecting back and forth the two fixed points in a two-dimensional auxiliary deterministic dynamical system. The escape rate is obtained, including the expression of the prefactor to van't Hoff-Arrhenius exponential factor./L'échappement des trajectoires est un phénomène omniprésent dans les systèmes dynamiques ouverts et les processus stochastiques. Si l'échappement se produit de façon répétitive pour un ensemble statistique de trajectoires, la population des trajectoires restantes subit souvent une décroissance exponentielle caractérisée par le taux d'échappement. L'inverse du taux d'échappement définit alors la durée de vie de l'état transitoire associé, ce qui représente une propriété intrinsèque du système. Ce paradigme est fondamental pour la théorie de la nucléation et, de manière générale, pour la théorie des taux de transitions en chimie, en physique et en biologie.
Dans de nombreux cas, l'échappement est induit par la présence de bruit, qui peut être d'origine interne ou externe. Ceci concerne en particulier l'échappement activé thermiquement à travers une barrière d'énergie potentielle, et plus généralement, l'échappement dû au bruit dans les systèmes dynamiques à temps continu ou à temps discret.
Dans la limite de faible bruit, on observe souvent une décroissance exponentielle du taux d'échappement en fonction de l'inverse de l'amplitude du bruit, un comportement qui est régi par la loi de van't Hoff-Arrhenius de la cinétique chimique. En particulier, les deux quantités importantes de cette loi sont le coefficient de la dépendance exponentielle (c'est-à-dire ``l'énergie d'activation') et son préfacteur.
L'objectif de cette thèse est de développer une théorie analytique pour déterminer ces deux quantités. La théorie que nous présentons concerne les systèmes unidimensionnels à temps continu ou discret perturbés par un bruit blanc gaussien et nous considérons le problème de l'échappement du bassin d'attraction d'un point fixe attractif. Pour s'échapper, les trajectoires du système bruité initialement contenues dans ce bassin d'attraction doivent alors traverser un point fixe instable qui forme la limite du bassin.
Dans le présent travail, et pour les deux types de systèmes, une formule est dérivée pour le taux d'échappement du point fixe attractif en utilisant des méthodes d'intégrales de chemin. Le calcul utilise la formule de trace pour les valeurs propres de l'opérateur gouvernant l'évolution temporelle de la densité de probabilité dans le système bruité. Le taux d'échappement est déterminé en considérant la boucle formée par deux orbites hétéroclines liant dans les deux sens les deux points fixes dans un système dynamique auxiliaire symplectique et bidimensionnel. On obtient alors le taux d'échappement, comprenant l'expression du préfacteur de l'exponentielle de la loi de van't Hoff-Arrhenius.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished
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Nguyen, Rémi. "Dynamic combinatorial mesophases and self-replicating systems." Strasbourg, 2010. http://www.theses.fr/2010STRA6285.
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Mon travail de thèse a consisté à développer des systèmes de blocs amphiphiles combinatoires dynamiques pour étudier de possibles phénomènes d’auto-organisation hiérarchique dans l’espace et dans le temps. Pour cela, j’ai combiné des associations réversibles de blocs hydrophiles et hydrophobes en étudiant deux types possibles de contrôle : a) un contrôle moléculaire externe sur les liaisons entre blocs de manière à forcer l’expression d’une mésophase particulière ; et b) un contrôle supramoléculaire interne dicté par la formation préférentielle d’une mésophase, avec sélection spontanée des blocs qui la composent. Lors de ce travail, j’ai pu démontrer pour la première fois la possibilité d’étendre la chimie combinatoire dynamique aux systèmes à micro-séparation de phase. Pour y parvenir, j’ai développé un nouveau type d’objets dynamiques (Dynablocks) et j’ai pu mettre en évidence des comportements très originaux de ces derniers qu’ils soient d’ordre cinétique (auto-réplication) ou thermodynamique (sélection au sein de mélange) ; j’ai également montré que ces deux aspects pouvaient être réunis au sein de processus d’auto-organisation. Pour caractériser les mélanges, de nouvelles méthodes de combinaisons linéaires pour l’analyse des diffusions du rayonnement ont été développées. Cette étude fondamentale constitue une nouvelle ouverture de la chimie combinatoire dynamique aux frontières avec deux domaines d’importance : a) la science des matériaux et b) la chimie des systèmes – en particulier des systèmes autonomes minimaux (i. E. Autopoiétiques)My PhD work consisted in developing combinatorial dynamic systems of amphiphilic block copolymers to study their hierarchical self-organization processes in space and time. For this I combined reversible associations between hydrophobic and hydrophilic blocks, focusing on two possible kinds of control of these responsive systems: a) an external molecular control on the reversible covalent bonds between the blocks in order to favour the expression of a particular mesophase; and b) an internal supramolecular control driven by the preferential formation of a mesophase leading to spontaneous selection of its own composing blocks. During this work, I demonstrated for the first time the possibility to extend dynamic combinatorial chemistry to systems with phase micro-separation. For this, I developed a new type of dynamic molecules (Dynablocks) and I discovered some interesting behaviours from the mesophases I obtained, such as self-replication on a kinetic point of view, or selection/adaptation process within a mixture on a thermodynamic point of view. I also demonstrated that these to aspects could be coupled together in an auto-organization process. To characterize those complex mixtures, new analytical methods were developed for scattering techniques, based on linear combinations. This fundamental study opens a new field of investigation for dynamic combinatorial chemistry in relations with two important domains: a) material science and b) system chemistry – particularly minimal autonomous systems (i. E. Autopoietics systems)
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Syzmczak, Andrzej. "Index pairs : from dynamics to combinatorics and back." Diss., Georgia Institute of Technology, 1999. http://hdl.handle.net/1853/28027.
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Ludlow, Richard Frederick. "Molecular networks : from dynamic combinatorial libraries to complex systems." Thesis, University of Cambridge, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.611116.
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Kwok, Terence 1973. "Neural networks with nonlinear system dynamics for combinatorial optimization." Monash University, School of Business Systems, 2001. http://arrow.monash.edu.au/hdl/1959.1/8928.
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Angelin, Marcus. "Discovery-Oriented Screening of Dynamic Systems: Combinatorial and Synthetic Applications." Doctoral thesis, KTH, Organisk kemi, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-12524.
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This thesis is divided into six parts, all centered around the development of dynamic (i.e., reversibly interacting) systems of molecules and their applications in dynamic combinatorial chemistry (DCC) and organic synthesis. Part one offers a general introduction, as well as a more detailed description of DCC, being the central concept of this thesis. Part two explores the potential of the nitroaldol reaction as a tool for constructing dynamic systems, employing benzaldehyde derivatives and nitroalkanes. This reaction is then applied in part three where a dynamic nitroaldol system is resolved by lipase-catalyzed transacylation, selecting two out of 16 components. In part four, reaction and crystallization driven DCC protocols are developed and demonstrated. The discovery of unexpected crystalline properties of certain pyridine β-nitroalcohols is used to resolve a dynamic system and further expanded into asynthetic procedure. Furthermore, a previously unexplored tandem nitroaldol-iminolactone rearrangement reaction between 2-cyanobenzaldehyde and primarynitroalkanes is used for the resolution of dynamic systems. It is also coupled with diastereoselective crystallization to demonstrate the possibility to combine several selection processes. The mechanism of this reaction is investigated and a synthetic protocol is developed for asymmetric synthesis of 3-substituted isoindolinones. Part five continues the exploration of tandem reactions by combining dynamic hemithioacetal or cyanohydrin formation with intramolecular cyclization to synthesize a wide range of 3-functionalized phthalides. Finally, part six deals with the construction of a laboratory experiment to facilitate the introduction of DCC in undergraduate chemistry education. The experiment is based on previous work in our group and features an acetylcholinesterase-catalyzed resolution of a dynamic transthioacylation system.QC 20100628
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Murfitt, Louise. "Discrete event dynamic systems in max-algebra : realisation and related combinatorial problems." Thesis, University of Birmingham, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.368451.
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Atcher, Ubiergo Joan. "Disulfide-based dynamic combinatorial libraries of macrocyclic pseudopeptides as bio-inspired complex chemical systems." Doctoral thesis, Universitat de Barcelona, 2015. http://hdl.handle.net/10803/305491.
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Dynamic combinatorial chemistry proposes the creation of a library of compounds (dynamic combinatorial library, DCL) inter-connected through reversible chemical processes. The concentrations in a DCL are determined by differences in the free energy between the constituents and, therefore, the variations in the composition of the library contain valuable information about changes in the stability of the members. The adaptive nature of DCLs can be intimately correlated with a very simple expression of molecular evolution.
The main objective of this thesis is to use DCLs as bio-inspired complex chemical systems for the minimalistic experimental modeling of different processes of biological interest.
In Chapter 1, fourteen new pseudopeptidic dithiols were designed, synthesized and fully characterized in order to be used as bipodal building blocks (BBs). Their design is based on a C2-symmetric scaffold consisting of a central m-phenylenediamine chromophore that rigidly joins two identical arms, each formed by an amino acid with a mercaptoacetyl moiety attached to the N-terminus. The pseudopeptidic nature provides the BBs with peptide-like information, differently charged functional groups and chiral information. In Chapter 2, suitable experimental conditions were developed for the generation of disulfide-based DCLs from the mixture of the synthesized BBs. For this purpose, the use of DMSO as a co-solvent has beneficial effects in the thiol-disulfide dynamic covalent chemistry. Apart from the general gain in the aqueous solubility of the organic molecules, it promotes the thiol oxidation, highly reducing the reaction time for the disulfide formation. Besides, it accelerates the disulfide exchange, allowing the system to fully equilibrate even at slightly acidic pH.
In Chapter 3, a minimalistic DCL was used to reproduce adaptive trends described for the evolution of biological systems. Thus, the addition of salt to a dynamic library of macrocyclic pseudopeptides induces the amplification of those species concentrating anionic amino acids, with the Asp derivatives showing a better salt-adaptation than the Glu counterparts. Structural studies suggest a folded conformation for the amplified members and reveal the selection of those species showing a smaller accessible surface area. The adaptive process is driven by the increase of the ionic strength and has a remarkable resemblance with the natural evolution of the proteins of halophilic microorganisms for surviving in hypersaline media. In Chapter 4, the same external stimulus was studied in a larger DCL consisting of 21 differently charged dimeric macrocycles. The salt-induced adaptation of this complex system was characterized in a top-down fashion by the dynamic deconvolution into the minimal components.
Additionally, structural studies were performed for selected species. The salt-response of the members of the library can be classified in different families attending to the charges, and the behavior of each member is determined by a combination of its structural information and the co-adaptive relationships with the other members of the complex network.
Finally, in Chapter 5, a simple DCL consisting of homo- and heterochiral dimeric pseudopeptides was used to study how the chiral information is transmitted from the molecular to the macromolecular level. A decrease in the polarity of the medium induces a homochiral self-sorting process driven by polar intramolecular interactions. Additionally, the homochiral selectivity also increases with the temperature, indicating a positive entropic contribution. Preliminary NMR experiments suggest significantly different conformations for the homo- and heterochiral species.
Overall, the adaptive nature of DCLs, together with a suitable bio-inspired design, have demonstrated to allow the minimalistic experimental modeling of different processes of biological interest such as the natural evolution of the halophilic proteins, the co-adaptive relationships in a complex network and the homochiral self-sorting phenomenon.Les quimioteques dinàmiques (DCLs de “dynamic combinatorial libraries”) estan formades per una mescla de compostos interconnectats per mitjà de processos químics reversibles. Aquests sistemes dinàmics presenten la capacitat d’adaptar la seva composició a la presència d’un estímul extern. L’objectiu principal d’aquesta tesi és utilitzar DCLs com a sistemes químics complexos pel modelatge experimental de diversos processos d’interès biològic. En el Capítol 1 es van dissenyar, sintetitzar i caracteritzar catorze ditiols amb informació estructural de tipus peptídic, cadenes laterals amb diferents càrregues i informació quiral. A continuació, en el Capítol 2, es van establir unes condicions experimentals adequades per a generar DCLs de disulfurs a partir de l’oxidació dels ditiols sintetitzats. En aquest sentit, l’ús de DMSO com a codissolvent orgànic va demostrar tenir una sèrie d’efectes beneficiosos. Seguidament, en el Capítol 3, es va utilitzar una DCL minimalista de disseny bioinspirat per a reproduir tendències adaptatives pròpies de processos evolutius biològics. Així, es va observar que els canvis que provoca l’increment de la salinitat en la composició d’una DCL de pseudopèptids macrocíclics, tenen una notable similitud amb l’evolució natural de les proteïnes dels microorganismes halòfils. En el Capítol 4 es va estudiar l’efecte del mateix estímul extern en la composició d’una DCL complexa formada per espècies amb diferents càrregues. S’evidencià que el comportament de cada membre de la quimioteca està determinat per la seva informació estructural i per les múltiples relacions coadaptatives que aquest estableix amb la resta de membres de la xarxa molecular. Finalment, en el Capítol 5, es va utilitzar una DCL minimalista formada per espècies estereoisomèriques per estudiar el fenomen d’autoordenació homoquiral.
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Larsson, Rikard. "Dynamic Systems for Screening, Control and Identification of Protein-Ligand Interactions." Doctoral thesis, Stockholm : Kemi, Chemistry, Kungliga Tekniska högskolan, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4709.
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Zhoroev, Tilekbek. "Controllability and Observability of Linear Nabla Discrete Fractional Systems." TopSCHOLAR®, 2019. https://digitalcommons.wku.edu/theses/3156.
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The main purpose of this thesis to examine the controllability and observability of the linear discrete fractional systems. First we introduce the problem and continue with the review of some basic definitions and concepts of fractional calculus which are widely used to develop the theory of this subject. In Chapter 3, we give the unique solution of the fractional difference equation involving the Riemann-Liouville operator of real order between zero and one. Additionally we study the sequential fractional difference equations and describe the way to obtain the state-space repre- sentation of the sequential fractional difference equations. In Chapter 4, we study the controllability and observability of time-invariant linear nabla fractional systems.We investigate the time-variant case in Chapter 5 and we define the state transition matrix in fractional calculus. In the last chapter, the results are summarized and directions for future work are stated.
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Schwarz, Felix Benjamin [Verfasser]. "Stimuli-Responsive Supramolecular Systems: From Dynamic Combinatorial Libraries to Photoswitchable Rotaxanes on Surfaces / Felix Benjamin Schwarz." Berlin : Freie Universität Berlin, 2017. http://d-nb.info/1125450347/34.
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Rotondo, Pablo. "Probabilistic studies in number theory and word combinatorics : instances of dynamical analysis." Thesis, Sorbonne Paris Cité, 2018. http://www.theses.fr/2018USPCC213/document.
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L'analyse dynamique intègre des outils propres aux systèmes dynamiques (comme l'opérateur de transfert) au cadre de la combinatoire analytique, et permet ainsi l'analyse d'un grand nombre d'algorithmes et objets qu'on peut associer naturellement à un système dynamique. Dans ce manuscrit de thèse, nous présentons, dans la perspective de l'analyse dynamique, l'étude probabiliste de plusieurs problèmes qui semblent à priori bien différents : l'analyse probabiliste de la fonction de récurrence des mots de Sturm, et l'étude probabiliste de l'algorithme du “logarithme continu”. Les mots de Sturm constituent une famille omniprésente en combinatoire des mots. Ce sont, dans un sens précis, les mots les plus simples qui ne sont pas ultimement périodiques. Les mots de Sturm ont déjà été beaucoup étudiés, notamment par Morse et Hedlund (1940) qui en ont exhibé une caractérisation fondamentale comme des codages discrets de droites à pente irrationnelle. Ce résultat relie ainsi les mots de Sturm au système dynamique d'Euclide. Les mots de Sturm n'avaient jamais été étudiés d'un point de vue probabiliste. Ici nous introduisons deux modèles probabilistes naturels (et bien complémentaires) et y analysons le comportement probabiliste (et asymptotique) de la “fonction de récurrence” ; nous quantifions sa valeur moyenne et décrivons sa distribution sous chacun de ces deux modèles : l'un est naturel du point de vue algorithmique (mais original du point de vue de l'analyse dynamique), et l'autre permet naturellement de quantifier des classes de plus mauvais cas. Nous discutons la relation entre ces deux modèles et leurs méthodes respectives, en exhibant un lien potentiel qui utilise la transformée de Mellin. Nous avons aussi considéré (et c'est un travail en cours qui vise à unifier les approches) les mots associés à deux familles particulières de pentes : les pentes irrationnelles quadratiques, et les pentes rationnelles (qui donnent lieu aux mots de Christoffel). L'algorithme du logarithme continu est introduit par Gosper dans Hakmem (1978) comme une mutation de l'algorithme classique des fractions continues. Il calcule le plus grand commun diviseur de deux nombres naturels en utilisant uniquement des shifts binaires et des soustractions. Le pire des cas a été étudié récemment par Shallit (2016), qui a donné des bornes précises pour le nombre d'étapes et a exhibé une famille d'entrées sur laquelle l'algorithme atteint cette borne. Dans cette thèse, nous étudions le nombre moyen d'étapes, tout comme d'autres paramètres importants de l'algorithme. Grâce à des méthodes d'analyse dynamique, nous exhibons des constantes mathématiques précises. Le système dynamique ressemble à première vue à celui d'Euclide, et a été étudié d'abord par Chan (2005) avec des méthodes ergodiques. Cependant, la présence des puissances de 2 dans les quotients change la nature de l'algorithme et donne une nature dyadique aux principaux paramètres de l'algorithme, qui ne peuvent donc pas être simplement caractérisés dans le monde réel.C'est pourquoi nous introduisons un nouveau système dynamique, avec une nouvelle composante dyadique, et travaillons dans ce système à deux composantes, l'une réelle, et l'autre dyadique. Grâce à ce nouveau système mixte, nous obtenons l'analyse en moyenne de l'algorithmeDynamical Analysis incorporates tools from dynamical systems, namely theTransfer Operator, into the framework of Analytic Combinatorics, permitting the analysis of numerous algorithms and objects naturally associated with an underlying dynamical system.This dissertation presents, in the integrated framework of Dynamical Analysis, the probabilistic analysis of seemingly distinct problems in a unified way: the probabilistic study of the recurrence function of Sturmian words, and the probabilistic study of the Continued Logarithm algorithm.Sturmian words are a fundamental family of words in Word Combinatorics. They are in a precise sense the simplest infinite words that are not eventually periodic. Sturmian words have been well studied over the years, notably by Morse and Hedlund (1940) who demonstrated that they present a notable number theoretical characterization as discrete codings of lines with irrationalslope, relating them naturally to dynamical systems, in particular the Euclidean dynamical system. These words have never been studied from a probabilistic perspective. Here, we quantify the recurrence properties of a ``random'' Sturmian word, which are dictated by the so-called ``recurrence function''; we perform a complete asymptotic probabilistic study of this function, quantifying its mean and describing its distribution under two different probabilistic models, which present different virtues: one is a naturaly choice from an algorithmic point of view (but is innovative from the point of view of dynamical analysis), while the other allows a natural quantification of the worst-case growth of the recurrence function. We discuss the relation between these two distinct models and their respective techniques, explaining also how the two seemingly different techniques employed could be linked through the use of the Mellin transform. In this dissertation we also discuss our ongoing work regarding two special families of Sturmian words: those associated with a quadratic irrational slope, and those with a rational slope (not properly Sturmian). Our work seems to show the possibility of a unified study.The Continued Logarithm Algorithm, introduced by Gosper in Hakmem (1978) as a mutation of classical continued fractions, computes the greatest common divisor of two natural numbers by performing division-like steps involving only binary shifts and substractions. Its worst-case performance was studied recently by Shallit (2016), who showed a precise upper-bound for the number of steps and gave a family of inputs attaining this bound. In this dissertation we employ dynamical analysis to study the average running time of the algorithm, giving precise mathematical constants for the asymptotics, as well as other parameters of interest. The underlying dynamical system is akin to the Euclidean one, and was first studied by Chan (around 2005) from an ergodic, but the presence of powers of 2 in the quotients ingrains into the central parameters a dyadic flavour that cannot be grasped solely by studying this system. We thus introduce a dyadic component and deal with a two-component system. With this new mixed system at hand, we then provide a complete average-case analysis of the algorithm by Dynamical Analysis
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Sakulsombat, Morakot. "Dynamic Systems: Evaluation, Screening and Synthetic Application." Doctoral thesis, KTH, Organisk kemi, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-34100.
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The research work reported in the thesis deals with the development of dynamic covalent systems and their applications in evaluation and screening of protein-ligands and enzyme inhibitors, as well as in synthetic methodologies. The thesis is divided into four parts as described below. In part one, synthetic methodologies to access 3-functionalized phthalides and 3-thioisoindolinones using the concept of cascade reactions are demonstrated. Efficient syntheses of the target products are designed and performed in one-pot process under mild reaction conditions. In part two, phosphine-catalyzed disulfide metathesis for the generation of dynamic carbohydrate system in aqueous solution is demonstrated. In the presence of biological target (Concanavalin A), the optimal dynamic ligand is successfully identified in situ by the 1H STD-NMR spectroscopy. In part three, lipase-catalyzed resolutions of dynamic reversible systems using reversible cyanohydrin and hemithioacetal reactions in one-pot processes are demonstrated. The dynamic systems are generated under thermodynamic control in organic solution and subsequently resolved by lipase-mediated resolution under kinetic control. The resolution processes resulted in the lipase-selected substrates with high structural and stereochemical specificities. In the last part, dynamic fragment-based strategy is presented using β-galactosidase as a model target enzyme. Based on our previous study, the best dynamic inhibitor of β-galactosidase was identified using 1H STD-NMR technique from dynamic hemithioacetal systems. The structure of the dynamic inhibitor is tailored by fragment linking and optimization processes. The designed inhibitor structures are then synthesized and tested for inhibition activities against β-galactosidase.QC 20110526
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Zhao, Kun. "Mathematical Methods for Network Analysis, Proteomics and Disease Prevention." Digital Archive @ GSU, 2012. http://digitalarchive.gsu.edu/math_diss/6.
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This dissertation aims at analyzing complex problems arising in the context of dynamical networks, proteomics, and disease prevention. First, a new graph-based method for proving global stability of synchronization in directed dynamical networks is developed. This method utilizes stability and graph theories to clarify the interplay between individual oscillator dynamics and network topology. Secondly, a graph-theoretical algorithm is proposed to predict Ca2+-binding site in proteins. The new algorithm enables us to identify previously-unknown Ca2+-binding sites, and deepens our understanding towards disease-related Ca2+-binding proteins at a molecular level. Finally, an optimization model and algorithm to solve a disease prevention problem are described at the population level. The new resource allocation model is designed to assist clinical managers to make decisions on identifying at-risk population groups, as well as selecting a screening and treatment strategy for chlamydia and gonorrhea patients under a fixed budget. The resource allocation model and algorithm can have a significant impact on real treatment strategy issues.
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Eryuzlu, Menevse. "Two Generalizations of the Filippov Operation." TopSCHOLAR®, 2016. http://digitalcommons.wku.edu/theses/1593.
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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.
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Dolce, Francesco. "Codes bifixes, combinatoire des mots et systèmes dynamiques symboliques." Thesis, Paris Est, 2016. http://www.theses.fr/2016PESC1036/document.
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L'étude des ensembles de mots complexité linéaire joue un rôle très important dans la théorie de combinatoire des mots et dans la théorie des systèmes dynamiques symboliques.Cette famille d'ensembles comprend les ensembles de facteurs : d'un mot Sturmien ou d'un mot d'Arnoux-Rauzy, d'un codage d'échange d'intervalle, d'un point fixe d'un morphisme primitif, etc.L'enjeu principal de cette thèse est l'étude de systèmes dynamiques minimales, définis de façon équivalente comme ensembles factoriels de mots uniformément récurrents.Comme résultat principal nous considérons une hiérarchie naturelle de systèmes minimal contenante les ensembles neutres, les tree sets et les ensembles spéculaires.De plus, on va relier ces systèmes au groupe libre en utilisant les mots de retours et les bases de sous-groupes d'indice fini.L'on étude aussi les systèmes symboliques dynamiques engendrés par les échanges d'intervalle et les involutions linéaires, ce qui nous permet d'obtenir des exemples et des interprétations géométriques des familles d'ensembles que définis dans notre hiérarchie.L'un des principal outil utilisé ici est l'étude des extensions possibles d'un mot dans un ensemble, ce qui nous permet de déterminer des propriétés telles que la complexité factorielle.Dans ce manuscrit, nous définissons le graphe d'extension, un graphe non orienté associé à chaque mot $w$ dans un ensemble $S$ qui décrit les extensions possibles de $w$ dans $S$ à gauche et à droite.Dans cette thèse, nous présentons plusieurs classes d'ensembles de mots définis par les formes possibles que les graphes d'extensions des éléments dans l'ensemble peuvent avoir.L'une des conditions les plus faibles que nous allons étudier est la condition de neutralité: un mot $w$ est neutre si le nombre de paires $(a,b)$ de lettres telles que $awb in S$ est égal au nombre de lettres $a$ tel que $aw in S$ plus le nombre de lettres $b$ tel que $wb in S$ moins 1.Un ensemble tel que chaque mot non vide satisfait la condition de neutralité est appelé un ensemble neutre.Une condition plus forte est la condition de l'arbre: un mot $w$ satisfait cette condition si son graphe d'extension est à la fois acyclique et connecté.Un ensemble est appelé un tree set si tout mot non vide satisfait cette condition.La famille de tree sets récurrents apparaît comme fermeture naturelle de deux familles d'ensembles très importants : les facteurs d'un mot d'Arnoux-Rauzy et les ensembles d'échange d'intervalle.Nous présentons également les ensembles spéculaires, une sous-famille remarquable de tree sets.Il s'agit également de sous-ensembles de groupes qui forment une généralisation naturelle des groupes libres.Ces ensembles de mots sont une généralisation abstraite des codages naturelles d'échanges d'intervalle et d'involutions linéaires.Pour chaque classe d'ensembles considéré dans cette thèse, nous montrons plusieurs résultats concernant les propriétés de fermeture (sous décodage maximale bifixe ou par rapport aux mots dérivés), la cardinalité des codes bifixes et les de mots de retour, la connexion entre mots de retour et bases du groupe libre, ainsi qu'entre les codes bifixes et les sous-groupes du groupe libre.Chacun de ces résultats est prouvé en utilisant les hypothèses les plus faibles possiblesSets of words of linear complexity play an important role in combinatorics on words and symbolic dynamics.This family of sets includes set of factors of Sturmian and Arnoux-Rauzy words, interval exchange sets and primitive morphic sets, that is, sets of factors of fixed points of primitive morphisms.The leading issue of this thesis is the study of minimal dynamical systems, also defined equivalently as uniformly recurrent sets of words.As a main result, we consider a natural hierarchy of minimal systems containing neutral sets, tree sets and specular sets.Moreover, we connect the minimal systems to the free group using the notions of return words and basis of subroups of finite index.Symbolic dynamical systems arising from interval exchanges and linear involutions provide us geometrical examples of this kind of sets.One of the main tool used here is the study of possible extensions of a word in a set, that allows us to determine properties such as the factor complexity.In this manuscript we define the extension graph, an undirected graph associated to each word $w$ in a set $S$ which describes the possible extensions of $w$ in $S$ on the left and the right.In this thesis we present several classes of sets of words defined by the possible shapes that the graphs of elements in the set can have.One of the weakest condition that we will study is the neutrality condition: a word $w$ is neutral if the number of pairs $(a, b)$ of letters such that $awb in S$ is equal to the number of letters $a$ such that $aw in S$ plus the number of letters $b$ such that $wb in S$ minus 1.A set such that every nonempty word satisfies the neutrality condition is called a neutral set.A stronger condition is the tree condition: a word $w$ satisfies this condition if its extension graph is both acyclic and connected.A set is called a tree set if any nonempty word satisfies this condition.The family of recurrent tree sets appears as a the natural closure of two known families, namely the Arnoux-Rauzy sets and the interval exchange sets.We also introduce specular sets, a remarkable subfamily of the tree sets.These are subsets of groups which form a natural generalization of free groups.These sets of words are an abstract generalization of the natural codings of interval exchanges and of linear involutions.For each class of sets considered in this thesis, we prove several results concerning closure properties (under maximal bifix decoding or under taking derived words), cardinality of the bifix codes and set of return words in these sets, connection between return words and basis of the free groups, as well as between bifix codes and subgroup of the free group.Each of these results is proved under the weakest possible assumptions
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Vongvilai, Pornrapee. "Dynamic Covalent Resolution: Applications in System Screening and Asymmetric Synthesis." Doctoral thesis, Stockholm : Skolan för kemivetenskap, Kungliga Tekniska högskolan, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-11200.
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Kyriakoglou, Revekka. "Morphismes itérés, combinatoire des mots et systèmes dynamiques symboliques." Thesis, Paris Est, 2019. http://www.theses.fr/2019PESC2050.
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La thèse actuelle porte sur le thème de la combinatoire des mots et des systèmes dynamiques symboliques. Les systèmes dynamiques symboliques sont des objets permettant de coder les trajectoires de mots dans des systèmes dynamiques de transformations d’espaces topologiques. Parmi ces systèmes dynamiques, des exemples bien connus sont donnés par des mots sturmiens et par d'échange d’intervalles. Les mots sturmiens sont liés à des algorithmes de géométrie discrète et l’échange d’intervalles forme une classe intéressante de systèmes dynamiques. En outre, il convient de mentionner que certaines familles d'échanges fournissent des généralisations prometteuses de mots sturmiens. Le sujet principal de la thèse est la reconnaissabilité des mots générés par les morphismes primitifs. Le concept de reconnaissabilité des morphismes trouve son origine dans l’article de Martin [1] sous le terme de détermination. Host a utilisé ce terme pour la première fois dans son article sur la théorie ergodique des systèmes dynamiques [2]. La notion de reconnaissabilité est apparue après lintêrt manifesté par de nombreux scientifiques pour ses diverses applications théoriques dans divers domaines, de la combinatoire des mots à la dynamique symbolique. Une notion similaire est celle de la circularit. Les deux termes sont souvent, mais pas toujours utilisés comme synonymes. Ce manque de cohérence dans la littérature pourrait être source de confusion. À la connaissance de l’auteur, il n’y a pas encore d’étude qui rassemble ces définitions et prouve leur équivalence ou indique les différences qui existent entre elles. Une approche solide de ce sujet, utilisant une définition cohérente de la reconnaissabilité et de la circularité. La notion de reconnaissabilité associée à une technique utilisée dans [3] a été utilisée afin de démontrer la décidabilité de différentes propriétés de graphes d’extension (définis dans [18]) d’éléments d’un langage. Les familles d’ensembles peuvent être définies à partir des propriétés du graphe d’extension de leurs éléments, tels que les ensembles acycliques, les ensembles d’arbres, les ensembles neutres, etc. Plus précisément, pour un ensemble de mots S, on peut associer à chaque mot w ∈ S son extension graphique qui décrit les extensions gauche et droite possibles de w dans S. Nous montrons comment utiliser la reconnaissabilité pour fournir la décidabilité des graphes d’extension. En outre, la notion de reconnaissance est utilisée dans lobjet de semigroupes profinite. Nous décrivons la relation entre la reconnaissabilité des morphismes et les propriétés des semigroupes profinites libres [5].Bibliography[1] John C. Martin. Minimal flows arising from substitutions of non-constant length. Math. Systems Theory, 7:72–82, 1973.[2] B. Host. Valeurs propres des systèmes dynamiques définis par des substitutions de longueur variable. Ergodic Theory Dynam. Systems, 6(4):529–540, 1986.[3] Klouda, K. and Starosta, Š. "Characterization of circular D0L systems", arXiv preprint arXiv:1401.0038 (2013).[4] Berthé, V., De Felice, C., Dolce, F. et al. Monatsh Math (2015) 176: 521. https://doi.org/10.1007/s00605-014-0721-4[5]Kyriakoglou ,R., Perrin ,D. "Profinite semigroups", arXiv:1703.10088 (2017)The current thesis focuses on the topic of combinatorics on words and symbolic dynamical systems. The symbolic dynamical systems are objects for encoding word trajectories in dynamic systems of transformations in topological spaces. Among these dynamical systems, well-known examples are given by Sturmial words and by exchange of intervals. The Sturmian words are related to discrete geometry algorithms and the exchange of intervals form an interesting class of dynamical systems. Furthermore, it should be mentioned that some exchange families provide promising generalizations of Sturmian words.The main subject of the thesis is the recognizability of words generated by primitive morphisms. The concept of recognizability of morphisms originates in the paper of Martin [1] under the term of determinization. The term was first used by Host in his paper on the Ergodic theory of Dynamical Systems[2]. The notion of recognizability came in full bloom after the interest shown by many scientists due to its various theoretical applications in various topics, from combinatorics on words to symbolic dynamics. A similar notion is that of circularity. The two terms are often, but not always used as synonymous. This lack of consistency along the literature could result in confusion. To the best of the author’s knowledge, there is not, as of yet, any study that collects those definitions and proves their equivalence or indicates the differences among them. This thesis provides a solid approach to this subject, using a coherent definition of recognizability and circularity.The notion of recognizability alongside a technique used in [3] were used in order to prove the decidability of different properties of extension graphs (defined in [4]) of elements of a language. Families of sets can be defined from properties of the extension graph of their elements, such as acyclic sets, tree sets, neutral sets, etc. More precisely, given a set of words S, one can associate with every word w ∈ S it's extension graph which describes the possible left and right extensions of w in S. We show how to use the recognizability to provide decidability of extension graphs. Furthermore, recognizability is used in is the subject of Profinite Semigroups. We describe the relationship between the recognizability of morphisms and properties of the free profinite semigroups [5].Bibliography[1] John C. Martin. Minimal flows arising from substitutions of non-constant length. Math. Systems Theory, 7:72–82, 1973.[2] B. Host. Valeurs propres des systèmes dynamiques définis par des substitu-tions de longueur variable. Ergodic Theory Dynam. Systems, 6(4):529–540,1986.[3] Klouda, K. and Starosta, Š. "Characterization of circular D0L systems.", arXiv preprint arXiv:1401.0038 (2013).[4] Berthé, V., De Felice, C., Dolce, F. et al. Monatsh Math (2015) 176: 521. https://doi.org/10.1007/s00605-014-0721-4[5]Kyriakoglou ,R., Perrin ,D. "Profinite semigroups", arXiv:1703.10088 (2017)[6]Almeida, J., "Profinite semigroups and applications" In Structural theory of automata, semigroups, and universal algebra, volume 207 of NATO Sci.43 Ser. II Math. Phys. Chem., pages 1–45. Springer, Dordrecht, 2005. Notes taken by Alfredo Costa
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França, Fabricio Olivetti de. "Algoritmos bio-inspirados aplicados a otimização dinamica." [s.n.], 2005. http://repositorio.unicamp.br/jspui/handle/REPOSIP/259091.
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Orientadores: Fernando Jose Von Zuben, Leandro Nunes de CastroDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação
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Resumo: Esta dissertação propõe algoritmos bio-inspirados para a solução de problemas de otimização dinâmica, ou seja, problemas em que a superfície de otimização no espaço de busca sofre variações diversas ao longo do tempo. Com a variação, no tempo, de número, posição e qualidade dos ótimos locais, as técnicas de programação matemática tendem a apresentar uma acentuada degradação de desempenho, pois geralmente foram concebidas para tratar do caso estático. Algoritmos populacionais, controle dinâmico do número de indivíduos na população, estratégias de busca local e uso eficaz de memória são requisitos desejados para o sucesso da otimização dinâmica, sendo contemplados nas propostas de solução implementadas nesta dissertação. Os algoritmos a serem apresentados e comparados com alternativas competitivas presentes na literatura são baseados em funcionalidades e estruturas de processamento de sistemas imunológicos e de colônias de formigas. Pelo fato de considerarem todos os requisitos para uma busca eficaz em ambientes dinâmicos, o desempenho dos algoritmos imuno-inspirados se mostrou superior em todos os critérios considerados para comparação dos resultados dos experimentos.
Abstract: This dissertation proposes bio-inspired algorithms to solve dynamic optimization problems, i.e., problems for which the optimization surface on the search space suffers several changes over time. With such variation of number, position and quality of local optima, mathematical programming techniques may present degradation of performance, because they were usually conceived to deal with static problems. Population-based algorithms, dynamic control of the population size, local search strategies and an efficient memory usage are desirable requirements to a proper treatment of dynamic optimization problems, thus being incorporated into the solution strategies implemented here. The algorithms to be presented, and compared with competitive alternatives available in the literature, are based on functionalities and processing structures of immune systems and ant colonies. Due to the capability of incorporating all the requirements for an efficient search on dynamic environments, the immune-inspired approaches overcome the others in all the performance criteria adopted to evaluate the experimental results.
Mestrado
Engenharia de Computação
Mestre em Engenharia Elétrica
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Vizcaino, González José Federico. "Estratégias para redução de perdas técnicas e melhoria nas condições de operação de redes de distribuição de energia elétrica." [s.n.], 2011. http://repositorio.unicamp.br/jspui/handle/REPOSIP/260382.
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Orientadores: Christiano Lyra Filho, Celso CavellucciTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação
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Resumo: O trabalho desenvolve alternativas de otimização combinatória para a redução de perdas técnicas e melhoria das condições de operação de sistemas de distribuição de energia elétrica. Sua principal contribuição é na área de redução dos fluxos de reativos através da instalação e controle de bancos de capacitores. Duas alternativas de otimização são desenvolvidas. A primeira, propõe um algoritmo genético híbrido com buscas locais nas representações fenotípicas e genotípicas das soluções. A segunda alternativa utiliza conceitos de programação dinâmica no projeto de algoritmos que encontram soluções ótimas globais para o problema de localização, dimensionamento e controle de capacitores. Outro algoritmo genético híbrido, para a instalação de reguladores de tensão, complementa a possibilidade de melhoria nos perfis de tensão proporcionada pelos capacitores. Os algoritmos baseados em programação dinâmica são de complexidade polinomial; adicionalmente, suas complexidades são lineares para instâncias reais. As características desses algoritmos estabelecem novas referências para a área de localização e controle de capacitores em sistemas de distribuição de energia elétrica, hoje povoada por métodos heurísticos
Abstract: This work develops combinatorial optimization alternatives for technical loss reduction and improvements on operational conditions of power distribution networks. Its main contribution is in the area of loss reduction by decreasing reactive flows, through allocation and control of shunt capacitors banks. Two optimization strategies are proposed. The first one develops a hybrid genetic algorithm with local searches in both genotypical and fenotypical representations of solutions. The second alternative uses dynamic programming concepts in the design of algorithms that unveil global optimal solutions for capacitor location, sizing and control. Another hybrid genetic algorithm for allocation of voltage regulators complements the improvement in voltage profiles obtained with the allocation of capacitors. The algorithms based on dynamic programming concepts have polynomial-time complexity; further, they have linear-time complexity for practical applications. Therefore, these algorithms establish a new reference for the area of shunt capacitors allocation and control on power distribution systems, which is today populated by heuristic methods
Doutorado
Energia Eletrica
Doutor em Engenharia Elétrica
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Voshell, Sharon M. Gagné Michel R. "Molecular recognition in synthetic systems I. Rigidified dendritic systems for imparting enantioselective molecular recognition to platinum-containing molecularly imprinted polymers II. Using laser polarimetry to identify an enantioselective receptor for (-)-adenosine from a racemic dynamic combinatorial library /." Chapel Hill, N.C. : University of North Carolina at Chapel Hill, 2006. http://dc.lib.unc.edu/u?/etd,618.
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Thesis (Ph. D.)--University of North Carolina at Chapel Hill, 2006.Title from electronic title page (viewed Oct. 10, 2007). "... in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Chemistry." Discipline: Chemistry; Department/School: Chemistry.
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Emme, Jordan. "Systèmes dynamiques substitutifs et renormalisation." Thesis, Aix-Marseille, 2016. http://www.theses.fr/2016AIXM4738.
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Ce travail de thèse porte sur l'étude de systèmes dynamiques substitutifs. Les substitutions ont historiquement été introduites pour décrire la suite des sommes des chiffres modulo 2 en base 2 . On étudie des propriétés de la suite somme des chiffres et notamment les propriétés des densités asymptotiques d'ensembles liés aux autocorrélations de fonctions arithmétiques définies par les fonctions somme des chiffres. On démontre notamment un théorème de la limite centrale pour ces densités. On étudie également les propriétés de régularité de la fonction de pression dans le cadre du formalisme thermodynamique, introduit par Bowen, Ruelle et Sinaï, pour une famille de potentiels définis en terme de distance à l'attracteur de la substitution de k-bonacci. On démontre la convergence des itérés de l'opérateur de renormalisation introduit par Baraviera, Leplaideur et Lopes vers un point fixe pour cette même famille de potentiels. Enfin, on étudie des propriétés de régularité de certaines mesures spectrales associées à des pavages auto-similaires en s'appuyant sur des travaux de Bufetov et Solomyak portant sur les déviations des sommes ergodiques dans le cas de l'action par translation de \R^d sur les pavages auto-similaires de R^d. On démontre qu'après renormalisation, ces mesures spectrales se comportent comme des mesures de Radon autour de zérIn the present work we study substitutive dynamical systems. Historically, substitutions have been introduced in order to describe the sequence of the sum-of-digits mod 2 in base 2. We study some properties of densities of sets defined by sum-of-digits functions, sets which are linked with autocorrelations of some arithmétic functions. We prove that these densities are usually normally distributed. We also study the regularity of the pressure function in the framework of the thermodynamics formalism, introduced by Bowen, Ruelle and Sinaï, for a family of potentials defined in terms of distance to the attractor of the k-bonacci substitution. We also show that the iterations of the renormalisation operator defined by Baraviera, Leplaideur and Lopes converges towards a fixed point of this operator. Finally we study the regularity of some spectral measures associated to self-similar tilings using mostly works from Bufetov and Solomyak on the deviations of ergodic sums for the action of translations by vectors in R^d on self-similar tilings of R^d. We prove that, afeter renormalisation, these spectral measures behave like Radon measures around
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Giscard, Pierre-Louis. "A graph theoretic approach to matrix functions and quantum dynamics." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:ceef15b0-eed2-4615-a9f2-f9efbef470c9.
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Many problems in applied mathematics and physics are formulated most naturally in terms of matrices, and can be solved by computing functions of these matrices. For example, in quantum mechanics, the coherent dynamics of physical systems is described by the matrix exponential of their Hamiltonian. In state of the art experiments, one can now observe such unitary evolution of many-body systems, which is of fundamental interest in the study of many-body quantum phenomena. On the other hand the theoretical simulation of such non-equilibrium many-body dynamics is very challenging. In this thesis, we develop a symbolic approach to matrix functions and quantum dynamics based on a novel algebraic structure we identify for sets of walks on graphs. We begin by establishing the graph theoretic equivalent to the fundamental theorem of arithmetic: all the walks on any finite digraph uniquely factorise into products of prime elements. These are the simple paths and simple cycles, walks forbidden from visiting any vertex more than once. We give an algorithm that efficiently factorises individual walks and obtain a recursive formula to factorise sets of walks. This yields a universal continued fraction representation for the formal series of all walks on digraphs. It only involves simple paths and simple cycles and is thus called a path-sum. In the second part, we recast matrix functions into path-sums. We present explicit results for a matrix raised to a complex power, the matrix exponential, matrix inverse, and matrix logarithm. We introduce generalised matrix powers which extend desirable properties of the Drazin inverse to all powers of a matrix. In the third part, we derive an intermediary form of path-sum, called walk-sum, relying solely on physical considerations. Walk-sum describes the dynamics of a quantum system as resulting from the coherent superposition of its histories, a discrete analogue to the Feynman path-integrals. Using walk-sum we simulate the dynamics of quantum random walks and of Rydberg-excited Mott insulators. Using path-sum, we demonstrate many-body Anderson localisation in an interacting disordered spin system. We give two observable signatures of this phenomenon: localisation of the system magnetisation and of the linear magnetic response function. Lastly we return to the study of sets of walks. We show that one can construct as many representations of series of walks as there are ways to define a walk product such that the factorisation of a walk always exist and is unique. Illustrating this result we briefly present three further methods to evaluate functions of matrices. Regardless of the method used, we show that graphs are uniquely characterised, up to an isomorphism, by the prime walks they sustain.
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Nguyen, Van Thé Lionel. "Théorie de Ramsey structurale et applications en dynamique topologique via la correspondance de Kechris-Pestov-Todorcevic." Habilitation à diriger des recherches, Aix-Marseille Université, 2013. http://tel.archives-ouvertes.fr/tel-00924106.
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Le but de ce mémoire est d'effectuer un survol de mes travaux effectués depuis janvier 2007. Le sujet d'étude se situe à l'une des intersections entre la combinatoire, la dynamique topologique et la logique via le formalisme des structures ultrahomogènes et de la théorie de Fraïssé. Ce domaine a récemment connu un essor considérable grâce à deux contributions majeures par Kechris, Pestov et Todorcevic, et par Kechris et Rosendal. Mon travail part de la première de ces contributions et se concentre autour des deux thèmes suivants : Théorie de Ramsey structurale et dynamique topologique des groupes de transformation associés.
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Vacher, Blandine. "Techniques d'optimisation appliquées au pilotage de la solution GTP X-PTS pour la préparation de commandes intégrant un ASRS." Thesis, Compiègne, 2020. http://www.theses.fr/2020COMP2566.
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Les travaux présentés dans ce document portent sur des problèmes d'optimisation dans le domaine de la logistique interne des entrepôts. Le domaine est soumis à une forte concurrence et est en plein essor, poussé par les besoins croissants du marché et favorisé par l'automatisation. L'entreprise SAVOYE construit des équipements et propose sa propre solution GTP (Goods-To-Person) pour la préparation de commandes. La solution utilise un système de stockage automatisé appelé X-Picking Tray System (X-PTS) et achemine les charges automatiquement à des postes de travail via des carrousels pour effectuer des opérations séquencées. C'est un système de systèmes particulièrement complexe qui offre de nombreuses applications aux techniques de la recherche opérationnelle. Tout cela définit le périmètre applicatif et théorique des travaux menés dans cette thèse. Nous avons d'abord traité un problème d'ordonnancement de type Job Shop avec des contraintes de précédences. Le contexte particulier du problème a permis de le résoudre en un temps polynomial avec un algorithme exact. Celui-ci a permis de calculer les dates d'injection des charges provenant des différents flux de sortie du stockage pour s'agréger sur un carrousel, dans un ordre donné. Ainsi, la gestion inter-allées du stockage PTS a été améliorée et le débit du flux de charges maximisé, depuis le stockage jusqu'à un poste. Nous avons ensuite étudié des algorithmes de tri tels que le tri par base et développé un algorithme de tri en ligne, utilisé pour piloter des systèmes autonomes de tri appelés Buffers Séquenceurs (BS). Placés en amont de chaque poste de travail dans la solution GTP, les BS permettent de délocaliser la fonction de tri en aval du stockage, augmentant de facto le débit des flux de sortie. Enfin, nous avons considéré un problème de séquencement consistant à trouver une extension linéaire d'un ordre partiel minimisant une distance avec un ordre donné. Nous proposons de le résoudre par une approche de programmation linéaire en nombres entiers, par la construction de programmes dynamiques et par des heuristiques de type glouton. Une heuristique efficace a été développée en se basant sur des appels itératifs d'un des programmes dynamiques, permettant d'atteindre une solution proche ou égale à l'optimum en un temps très court. L'application de ce problème aux flux de sortie non ordonnés du stockage X-PTS permet de réaliser un pré-tri au niveau des carrousels. Les diverses solutions développées ont été validées par simulation et certaines ont été brevetées et/ou déjà été mises en application dans des entrepôtsThe work presented in this PhD thesis deals with optimization problems in the context of internal warehouse logistics. The field is subject to strong competition and extensive growth, driven by the growing needs of the market and favored by automation. SAVOYE builds warehouse storage handling equipment and offers its own GTP (Goods-To-Person) solution for order picking. The solution uses an Automated Storage and Retrieval System (ASRS) called X-Picking Tray System (X-PTS) and automatically routes loads to workstations via carousels to perform sequenced operations. It is a highly complex system of systems with many applications for operational research techniques. All this defines the applicative and theoretical scope of the work carried out in this thesis. In this thesis, we have first dealt with a specific scheduling Job Shop problem with precedence constraints. The particular context of this problem allowed us to solve it in polynomial time with exact algorithms. These algorithms made it possible to calculate the injection schedule of the loads coming from the different storage output streams to aggregate on a carousel in a given order. Thus, the inter-aisle management of the X-PTS storage was improved and the throughput of the load flow was maximized, from the storage to a station. In the sequel of this work, the radix sort LSD (Least Significant Digit) algorithm was studied and a dedicated online sorting algorithm was developed. The second one is used to drive autonomous sorting systems called Buffers Sequencers (BS), which are placed upstream of each workstation in the GTP solution. Finally, a sequencing problem was considered, consisting of finding a linear extension of a partial order minimizing a distance with a given order. An integer linear programming approach, different variants of dynamic programming and greedy algorithms were proposed to solve it. An efficient heuristic was developed based on iterative calls of dynamic programming routines, allowing to reach a solution close or equal to the optimum in a very short time. The application of this problem to the unordered output streams of X-PTS storage allows pre-sorting at the carousel level. The various solutions developed have been validated by simulation and some have been patented and/or already implemented in warehouses
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Al-Hasani, Firas Ali Jawad. "Multiple Constant Multiplication Optimization Using Common Subexpression Elimination and Redundant Numbers." Thesis, University of Canterbury. Electrical and Computer Engineering, 2014. http://hdl.handle.net/10092/9054.
Full textAbstract:
The multiple constant multiplication (MCM) operation is a fundamental operation in digital signal processing (DSP) and digital image processing (DIP). Examples of the MCM are in finite impulse response (FIR) and infinite impulse response (IIR) filters, matrix multiplication, and transforms.
The aim of this work is minimizing the complexity of the MCM operation using common subexpression elimination (CSE) technique and redundant number representations. The CSE technique searches and eliminates common digit patterns (subexpressions) among MCM coefficients. More common subexpressions can be found by representing the MCM coefficients using redundant number representations.
A CSE algorithm is proposed that works on a type of redundant numbers called the zero-dominant set (ZDS). The ZDS is an extension over the representations of minimum number of non-zero digits called minimum Hamming weight (MHW). Using the ZDS improves CSE algorithms' performance as compared with using the MHW representations. The disadvantage of using the ZDS is it increases the possibility of overlapping patterns (digit collisions). In this case, one or more digits are shared between a number of patterns. Eliminating a pattern results in losing other patterns because of eliminating the common digits. A pattern preservation algorithm (PPA) is developed to resolve the overlapping patterns in the representations.
A tree and graph encoders are proposed to generate a larger space of number representations. The algorithms generate redundant representations of a value for a given digit set, radix, and wordlength. The tree encoder is modified to search for common subexpressions simultaneously with generating of the representation tree. A complexity measure is proposed to compare between the subexpressions at each node. The algorithm terminates generating the rest of the representation tree when it finds subexpressions with maximum sharing. This reduces the search space while minimizes the hardware complexity.
A combinatoric model of the MCM problem is proposed in this work. The model is obtained by enumerating all the possible solutions of the MCM that resemble a graph called the demand graph. Arc routing on this graph gives the solutions of the MCM problem. A similar arc routing is found in the capacitated arc routing such as the winter salting problem. Ant colony optimization (ACO) meta-heuristics is proposed to traverse the demand graph. The ACO is simulated on a PC using Python programming language. This is to verify the model correctness and the work of the ACO. A parallel simulation of the ACO is carried out on a multi-core super computer using C++ boost graph library.
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Waserhole, Ariel. "Optimisation des systèmes de véhicules en libre service par la tarification." Thesis, Grenoble, 2013. http://www.theses.fr/2013GRENM049/document.
Full textAbstract:
Nous étudions les systèmes de véhicules en libre service en aller-simple : avec emprunt et restitution dans des lieux éventuellement différents. La publicité promeut l'image de flexibilité et d'accessibilité (tarifaire) de tels systèmes, mais en réalité il arrive qu'il n'y ait pas de véhicule disponible au départ, voire pire, pas de place à l'arrivée. Il est envisageable (et pratiqué pour Vélib' à Paris) de relocaliser les véhicules pour éviter que certaines stations soient vides ou pleines à cause des marées ou de la gravitation. Notre parti-pris est cependant de ne pas considérer de ``relocalisation physique'' (à base de tournées de camions) en raison du coût, du trafic et de la pollution occasionnées (surtout pour des systèmes de voitures, comme Autolib' à Paris). La question à laquelle nous désirons répondre dans cette thèse est la suivante : Une gestion via des tarifs incitatifs permet-elle d'améliorer significativement les performances des systèmes de véhicules en libre service ?One way Vehicle Sharing Systems (VSS), in which users pick-up and return a vehicle in different places is a new type of transportation system that presents many advantages. However, even if advertising promotes an image of flexibility and price accessibility, in reality customers might not find a vehicle at the original station (which may be considered as an infinite price), or worse, a parking spot at destination. Since the first Bike Sharing Systems (BSS), problems of vehicles and parking spots availability have appeared crucial. We define the system performance as the number of trips sold (to be maximized). BSS performance is currently improved by vehicle relocation with trucks. Our scope is to focus on self regulating systems through pricing incentives, avoiding physical station balancing. The question we are investigating in this thesis is the following: Can a management of the incentives increases significantly the performance of the vehicle sharing systems?
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"ANALYSIS AND PREDICTION OF GENE EXPRESSION PATTERNS BY DYNAMICAL SYSTEMS, AND BY A COMBINATORIAL ALGORITHM." Master's thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/12606672/index.pdf.
Full text
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(8422929), Ivan Chio. "Some Connections Between Complex Dynamics and Statistical Mechanics." Thesis, 2020.
Find full textAbstract:
Associated to any finite simple graph Γ is the chromatic polynomial PΓ(q) whose complex zeros are called the chromatic zeros of Γ. A hierarchical lattice is a sequence of finite simple graphs {Γn}∞n-0 built recursively using a substitution rule expressed in terms of a generating graph. For each n, let μn denote the probability measure that assigns a Dirac measure to each chromatic zero of Γn. Under a mild hypothesis on the generating graph, we prove that the sequence μn converges to some measure μ as n tends to infinity. We call μ the limiting measure of chromatic zeros associated to {Γn}∞n-0. In the case of the Diamond Hierarchical Lattice we prove that the support of μ has Hausdorff dimension two.The main techniques used come from holomorphic dynamics and more specifically the theories of activity/bifurcation currents and arithmetic dynamics. We prove anew equidistribution theorem that can be used to relate the chromatic zeros of ahierarchical lattice to the activity current of a particular marked point. We expect that this equidistribution theorem will have several other applications, and describe one such example in statistical mechanics about the Lee-Yang-Fisher zeros for the Cayley Tree.
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"A genetic algorithm + dynamic programming solution for unit commitment problem." Chinese University of Hong Kong, 1996. http://library.cuhk.edu.hk/record=b5888990.
Full textAbstract:
by Lo Kam Ming.Thesis (M.Phil.)--Chinese University of Hong Kong, 1996.
Includes bibliographical references (leaves 107-111).
Chapter 1 --- Introduction --- p.7
Chapter 1.1 --- The Goal --- p.8
Chapter 1.2 --- The Work of the Thesis --- p.9
Chapter 1.3 --- Layout of Thesis --- p.9
Chapter 2 --- The Unit Commitment Problem --- p.11
Chapter 2.1 --- What is UCP? --- p.11
Chapter 2.1.1 --- Why is UCP difficult? --- p.12
Chapter 2.1.2 --- Costs --- p.12
Chapter 2.1.3 --- Constraints --- p.13
Chapter 2.2 --- Mathematical Formulation --- p.15
Chapter 2.3 --- Literature Review --- p.19
Chapter 2.3.1 --- Exhaustive Enumeration --- p.19
Chapter 2.3.2 --- Priority List --- p.20
Chapter 2.3.3 --- Langragian Relaxation --- p.21
Chapter 2.3.4 --- Neural Network --- p.21
Chapter 2.3.5 --- Genetic Algorithms --- p.22
Chapter 2.3.6 --- Dynamic Programming --- p.22
Chapter 3 --- Genetic Algorithms --- p.24
Chapter 3.1 --- Introduction --- p.24
Chapter 3.1.1 --- Outline of Traditional GA --- p.25
Chapter 3.2 --- Basic elements --- p.26
Chapter 3.2.1 --- Coding --- p.26
Chapter 3.2.2 --- Fitness Function --- p.26
Chapter 3.2.3 --- Selection and Reproduction --- p.26
Chapter 3.2.4 --- Mutation --- p.28
Chapter 3.2.5 --- Replacement --- p.29
Chapter 3.2.6 --- Epistasis --- p.29
Chapter 3.2.7 --- A Simple Example --- p.30
Chapter 3.3 --- Exploration vs Exploitation --- p.33
Chapter 3.4 --- Constraints Handlings --- p.34
Chapter 3.4.1 --- Penalty Function --- p.35
Chapter 3.4.2 --- Proper Encoding --- p.36
Chapter 3.4.3 --- Repair Algorithms --- p.36
Chapter 4 --- Dynamic Programming --- p.37
Chapter 4.1 --- Introduction --- p.37
Chapter 4.1.1 --- Decomposition --- p.38
Chapter 4.2 --- Mathematical Formulation --- p.43
Chapter 4.3 --- A Simple Example --- p.44
Chapter 5 --- DP Crossover Operator (DPX) --- p.50
Chapter 5.1 --- Why DP is chosen as the crossover operator --- p.50
Chapter 5.2 --- What is DPX? --- p.51
Chapter 5.2.1 --- A Simple Example --- p.51
Chapter 5.2.2 --- Mechanism of DPX --- p.58
Chapter 5.3 --- Properties of DPX --- p.63
Chapter 5.3.1 --- Number of parents --- p.63
Chapter 5.3.2 --- Crossover Sites --- p.65
Chapter 5.3.3 --- Perservation of Feasibility --- p.66
Chapter 6 --- Implementation --- p.69
Chapter 6.1 --- GA Construction --- p.69
Chapter 6.1.1 --- Coding --- p.69
Chapter 6.1.2 --- Fitness Function --- p.70
Chapter 6.1.3 --- Selection --- p.72
Chapter 6.1.4 --- Crossover --- p.76
Chapter 6.1.5 --- Mutation Rate --- p.76
Chapter 6.1.6 --- Replacement --- p.77
Chapter 6.2 --- Algorithm --- p.77
Chapter 6.3 --- Optimal Power Generations for Fuel Costs --- p.80
Chapter 6.3.1 --- The Simple Scheduling Method --- p.80
Chapter 7 --- Experimental Results --- p.84
Chapter 7.1 --- Experiment Details --- p.84
Chapter 7.2 --- Problem A --- p.86
Chapter 7.2.1 --- Data Results --- p.86
Chapter 7.2.2 --- Graphical Results --- p.90
Chapter 7.2.3 --- Analysis --- p.90
Chapter 7.3 --- Problem B --- p.92
Chapter 7.3.1 --- Data Results --- p.92
Chapter 7.3.2 --- Graphical Results --- p.94
Chapter 7.3.3 --- Analysis --- p.96
Chapter 8 --- Conclusion and Future Work --- p.97
Chapter 8.1 --- Conclusion --- p.97
Chapter 8.2 --- Future Work --- p.98
Chapter A --- Problems Parameters --- p.100
Chapter A.1 --- Problem A --- p.100
Chapter A.1.1 --- Parameters of Generating Units --- p.101
Chapter A.2 --- Problem B --- p.103
Chapter A.2. --- 1 Parameters of Generating Units --- p.104
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Terekhov, Daria. "Integrating Combinatorial Scheduling with Inventory Management and Queueing Theory." Thesis, 2013. http://hdl.handle.net/1807/36017.
Full textAbstract:
The central thesis of this dissertation is that by combining classical scheduling methodologies with those of inventory management and queueing theory we can better model, understand and solve complex real-world scheduling problems. In part II of this dissertation, we provide models of a realistic supply chain scheduling problem that capture both its combinatorial nature and its dependence on inventory availability. We present an extensive empirical evaluation of how well implementations of these models in commercially available software solve the problem. We are therefore able to address, within a specific problem, the need for scheduling to take into account related decision-making processes. In order to simultaneously deal with combinatorial and dynamic properties of real scheduling problems, in part III we propose to integrate queueing theory and deterministic scheduling. Firstly, by reviewing the queueing theory literature that deals with dynamic resource allocation and sequencing and outlining numerous future work directions, we build a strong foundation for the investigation of the integration of queueing theory and scheduling. Subsequently, we demonstrate that integration can take place on three levels: conceptual, theoretical and algorithmic. At the conceptual level, we combine concepts, ideas and problem settings from the two areas, showing that such combinations provide insights into the trade-off between long-run and short-run objectives. Next, we show that theoretical integration of queueing and scheduling can lead to long-run performance guarantees for scheduling algorithms that have previously been proved only for queueing policies. In particular, we are the first to prove, in two flow shop environments, the stability of a scheduling method that is based on the traditional scheduling literature and utilizes processing time information to make sequencing decisions. Finally, to address the algorithmic level of integration, we present, in an extensive future work chapter, one general approach for creating hybrid queueing/scheduling algorithms. To our knowledge, this dissertation is the first work that builds a framework for integrating queueing theory and scheduling. Motivated by characteristics of real problems, this dissertation takes a step toward extending scheduling research beyond traditional assumptions and addressing more realistic scheduling problems.
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Aramon, Bajestani Maliheh. "Integrating Maintenance Planning and Production Scheduling: Making Operational Decisions with a Strategic Perspective." Thesis, 2014. http://hdl.handle.net/1807/65637.
Full textAbstract:
In today's competitive environment, the importance of continuous production, quality improvement, and fast delivery has forced production and delivery processes to become highly reliable. Keeping equipment in good condition through maintenance activities can ensure a more reliable system. However, maintenance leads to temporary reduction in capacity that could otherwise be utilized for production. Therefore, the coordination of maintenance and production is important to guarantee good system performance. The central thesis of this dissertation is that integrating maintenance and production decisions increases efficiency by ensuring high quality production, effective resource utilization, and on-time deliveries.
Firstly, we study the problem of integrated maintenance
and production planning where machines are preventively maintained in the context of a periodic review production system with uncertain yield. Our goal is to provide insight into the optimal maintenance policy, increasing the number of finished products. Specifically, we prove the conditions that guarantee the optimal maintenance policy has a threshold type.
Secondly, we address the problem of integrated maintenance
planning and production scheduling where machines are correctively maintained in the context of a dynamic aircraft repair shop. To solve the problem, we view the dynamic repair shop as successive static repair scheduling sub-problems over shorter periods. Our results show that the approach that uses logic-based Benders decomposition to solve the static sub-problems, schedules over longer horizon, and quickly adjusts the schedule increases the utilization of aircraft in the long term.
Finally, we tackle the problem of integrated maintenance planning and production scheduling where machines are preventively maintained in the context of a multi-machine production system. Depending on the deterioration process of machines, we design decomposed techniques that deal with the stochastic and combinatorial challenges in different, coupled stages. Our results demonstrate that the integrated approaches decrease the total maintenance and lost production cost, maximizing the on-time deliveries. We also prove sufficient conditions that guarantee the monotonicity of the optimal maintenance policy in both machine state and the number of customer orders.
Within these three contexts, this dissertation demonstrates that the integrated maintenance and production decision-making increases the process efficiency to produce high quality products in a timely manner.