Dissertations / Theses on the topic 'Markov algebras'
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Black, Samson 1979. "Representations of Hecke algebras and the Alexander polynomial." Thesis, University of Oregon, 2010. http://hdl.handle.net/1794/10847.
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viii, 50 p. : ill. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number.We study a certain quotient of the Iwahori-Hecke algebra of the symmetric group Sd , called the super Temperley-Lieb algebra STLd. The Alexander polynomial of a braid can be computed via a certain specialization of the Markov trace which descends to STLd. Combining this point of view with Ocneanu's formula for the Markov trace and Young's seminormal form, we deduce a new state-sum formula for the Alexander polynomial. We also give a direct combinatorial proof of this result.
Committee in charge: Arkady Vaintrob, Co-Chairperson, Mathematics Jonathan Brundan, Co-Chairperson, Mathematics; Victor Ostrik, Member, Mathematics; Dev Sinha, Member, Mathematics; Paul van Donkelaar, Outside Member, Human Physiology
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Milios, Dimitrios. "On approximating the stochastic behaviour of Markovian process algebra models." Thesis, University of Edinburgh, 2014. http://hdl.handle.net/1842/8930.
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Markov chains offer a rigorous mathematical framework to describe systems that exhibit stochastic behaviour, as they are supported by a plethora of methodologies to analyse their properties. Stochastic process algebras are high-level formalisms, where systems are represented as collections of interacting components. This compositional approach to modelling allows us to describe complex Markov chains using a compact high-level specification. There is an increasing need to investigate the properties of complex systems, not only in the field of computer science, but also in computational biology. To explore the stochastic properties of large Markov chains is a demanding task in terms of computational resources. Approximating the stochastic properties can be an effective way to deal with the complexity of large models. In this thesis, we investigate methodologies to approximate the stochastic behaviour of Markovian process algebra models. The discussion revolves around two main topics: approximate state-space aggregation and stochastic simulation. Although these topics are different in nature, they are both motivated by the need to efficiently handle complex systems. Approximate Markov chain aggregation constitutes the formulation of a smaller Markov chain that approximates the behaviour of the original model. The principal hypothesis is that states that can be characterised as equivalent can be adequately represented as a single state. We discuss different notions of approximate state equivalence, and how each of these can be used as a criterion to partition the state-space accordingly. Nevertheless, approximate aggregation methods typically require an explicit representation of the transition matrix, a fact that renders them impractical for large models. We propose a compositional approach to aggregation, as a means to efficiently approximate complex Markov models that are defined in a process algebra specification, PEPA in particular. Regarding our contributions to Markov chain simulation, we propose an accelerated method that can be characterised as almost exact, in the sense that it can be arbitrarily precise. We discuss how it is possible to sample from the trajectory space rather than the transition space. This approach requires fewer random samples than a typical simulation algorithm. Most importantly, our approach does not rely on particular assumptions with respect to the model properties, in contrast to otherwise more efficient approaches.
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Johnston, Ann. "Markov Bases for Noncommutative Harmonic Analysis of Partially Ranked Data." Scholarship @ Claremont, 2011. http://scholarship.claremont.edu/hmc_theses/4.
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Given the result $v_0$ of a survey and a nested collection of summary statistics that could be used to describe that result, it is natural to ask which of these summary statistics best describe $v_0$. In 1998 Diaconis and Sturmfels presented an approach for determining the conditional significance of a higher order statistic, after sampling a space conditioned on the value of a lower order statistic. Their approach involves the computation of a Markov basis, followed by the use of a Markov process with stationary hypergeometric distribution to generate a sample.This technique for data analysis has become an accepted tool of algebraic statistics, particularly for the study of fully ranked data. In this thesis, we explore the extension of this technique for data analysis to the study of partially ranked data, focusing on data from surveys in which participants are asked to identify their top $k$ choices of $n$ items. Before we move on to our own data analysis, though, we present a thorough discussion of the Diaconis–Sturmfels algorithm and its use in data analysis. In this discussion, we attempt to collect together all of the background on Markov bases, Markov proceses, Gröbner bases, implicitization theory, and elimination theory, that is necessary for a full understanding of this approach to data analysis.
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Cothren, Jackson D. "Reliability in constrained Gauss-Markov models an analytical and differential approach with applications in photogrammetry /." Connect to this title online, 2004. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1085689960.
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Thesis (Ph. D.)--Ohio State University, 2004.Title from first page of PDF file. Document formatted into pages; contains xii, 119 p.; also includes graphics (some col.). Includes bibliographical references (p. 106-109). Available online via OhioLINK's ETD Center
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Farlow, Kasie Geralyn. "Max-Plus Algebra." Thesis, Virginia Tech, 2009. http://hdl.handle.net/10919/32191.
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In max-plus algebra we work with the max-plus semi-ring which is the set ℝmax=[-∞)∪ℝ together with operations 𝑎⊕𝑏 = max(𝑎,𝑏) and 𝑎⊗𝑏= 𝑎+𝑏. The additive and multiplicative identities are taken to be ε=-∞ and ε=0 respectively. Max-plus algebra is one of many idempotent semi-rings which have been considered in various fields of mathematics. Max-plus algebra is becoming more popular not only because its operations are associative, commutative and distributive as in conventional algebra but because it takes systems that are non-linear in conventional algebra and makes them linear. Max-plus algebra also arises as the algebra of asymptotic growth rates of functions in conventional algebra which will play a significant role in several aspects of this thesis. This thesis is a survey of max-plus algebra that will concentrate on max-plus linear algebra results. We will then consider from a max-plus perspective several results by Wentzell and Freidlin for finite state Markov chains with an asymptotic dependence.Master of Science
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Castro, Gilles Gonçalves de. "C*-álgebras associadas a certas dinâmicas e seus estados KMS." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2009. http://hdl.handle.net/10183/18824.
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D'abord, on étudie trois façons d'associer une C*-algèbre à une transformation continue. Ensuite, nous donnons une nouvelle définition de l'entropie. Nous trouvons des relations entre les états KMS des algèbres préalablement définies et les états d'équilibre, donné par un principe variationnel. Dans la seconde partie, nous étudions les algèbres de Kajiwara-Watatani associees a un système des fonctions itérées. Nous comparons ces algèbres avec l'algèbre de Cuntz et le produit croisé. Enfin, nous étudions les états KMS des algèbres de Kajiwara-Watatani pour les actions provenant d'un potentiel et nous trouvouns des relations entre ces états et les mesures trouvee dans une version de le théorème de Ruelle-Perron-Frobenius pour les systèmes de fonctions itérées.Primeiramente, estudamos três formas de associar uma C*-álgebra a uma transformação contínua. Em seguida, damos uma nova definição de entropia. Relacionamos, então, os estados KMS das álgebras anteriormente definidas com os estados de equilibro, vindos de um princípio variacional. Na segunda parte, estudamos as álgebras de Kajiwara-Watatani associadas a um sistema de funções iteradas. Comparamos tais álgebras com a álgebra de Cuntz e a álgebra do produto cruzado. Finalmente, estudamos os estados KMS das álgebras de Kajiwara-Watatani para ações vindas de um potencial e relacionamos tais estados KMS com medidas encontradas numa versão do teorema de Ruelle-Perron-Frobenius para sistemas de funções iteradas.
First, we study three ways of associating a C*-algebra to a continuous map. Then, we give a new de nition of entropy. We relate the KMS states of the previously de ned algebras with the equilibrium states, given by a variational principle. In the second part, we study the Kajiwara-Watatani algebras associated to iterated function system. We compare these algebras with the Cuntz algebra and the crossed product. Finally, we study the KMS states of the Kajiwara-Watatani algebras for actions coming from a potential and we relate such states with measures found in a version of the Ruelle-Perron- Frobenius theorem for iterated function systems.
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Orellana, Rosa C. "The Hecke algebra of type B at roots of unity, Markov traces and subfactors /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 1999. http://wwwlib.umi.com/cr/ucsd/fullcit?p9938595.
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Tribastone, Mirco. "Scalable analysis of stochastic process algebra models." Thesis, University of Edinburgh, 2010. http://hdl.handle.net/1842/4629.
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The performance modelling of large-scale systems using discrete-state approaches is fundamentally hampered by the well-known problem of state-space explosion, which causes exponential growth of the reachable state space as a function of the number of the components which constitute the model. Because they are mapped onto continuous-time Markov chains (CTMCs), models described in the stochastic process algebra PEPA are no exception. This thesis presents a deterministic continuous-state semantics of PEPA which employs ordinary differential equations (ODEs) as the underlying mathematics for the performance evaluation. This is suitable for models consisting of large numbers of replicated components, as the ODE problem size is insensitive to the actual population levels of the system under study. Furthermore, the ODE is given an interpretation as the fluid limit of a properly defined CTMC model when the initial population levels go to infinity. This framework allows the use of existing results which give error bounds to assess the quality of the differential approximation. The computation of performance indices such as throughput, utilisation, and average response time are interpreted deterministically as functions of the ODE solution and are related to corresponding reward structures in the Markovian setting. The differential interpretation of PEPA provides a framework that is conceptually analogous to established approximation methods in queueing networks based on meanvalue analysis, as both approaches aim at reducing the computational cost of the analysis by providing estimates for the expected values of the performance metrics of interest. The relationship between these two techniques is examined in more detail in a comparison between PEPA and the Layered Queueing Network (LQN) model. General patterns of translation of LQN elements into corresponding PEPA components are applied to a substantial case study of a distributed computer system. This model is analysed using stochastic simulation to gauge the soundness of the translation. Furthermore, it is subjected to a series of numerical tests to compare execution runtimes and accuracy of the PEPA differential analysis against the LQN mean-value approximation method. Finally, this thesis discusses the major elements concerning the development of a software toolkit, the PEPA Eclipse Plug-in, which offers a comprehensive modelling environment for PEPA, including modules for static analysis, explicit state-space exploration, numerical solution of the steady-state equilibrium of the Markov chain, stochastic simulation, the differential analysis approach herein presented, and a graphical framework for model editing and visualisation of performance evaluation results.
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Silva, Carlos Eduardo Vitória da. "Aplicações da álgebra linear nas cadeias de Markov." Universidade Federal de Goiás, 2013. http://repositorio.bc.ufg.br/tede/handle/tede/3480.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
The theory of linear algebra and matrices and systems particularly are linear math topics that can be applied not only within mathematics itself, but also in various other areas of human knowledge, such as physics, chemistry, biology, all engineering, psychology, economy, transportation, administration, statistics and probability, etc... The Markov chains are used to solve certain problems in the theory of probability. Applications of Markov chains in these problems, depend directly on the theory of matrices and linear systems. In this work we use the techniques of Markov Chains to solve three problems of probability, in three distinct areas. One in genetics, other in psychology and the other in the area of mass transit in a transit system. All work is developed with the intention that a high school student can read and understand the solutions of three problems presented.
A teoria da álgebra linear e particularmente matrizes e sistemas lineares são tópicos de matemática que podem ser aplicados não só dentro da própria matemática, mas também em várias outras áreas do conhecimento humano, como física, química, biologia, todas as engenharias, psicologia, economia, transporte, administração, estat ística e probabilidade, etc. As Cadeias de Markov são usadas para resolver certos problemas dentro da teoria das probabilidades. As aplicações das Cadeias de Markov nesses problemas, dependem diretamente da teoria das matrizes e sistemas lineares. Neste trabalho usamos as técnicas das Cadeias de Markov para resolver três problemas de probabilidades, em três áreas distintas. Um na área da genética, outro na área da psicologia e o outro na área de transporte de massa em um sistema de trânsito. Todo o trabalho é desenvolvido com a intenção de que um estudante do ensino médio possa ler e entender as soluções dos três problemas apresentados.
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Louise, Stéphane. "Calcul de majorants sûrs de temps d'exécution au pire pour des tâches d'applications temps-réels critiques, pour des systèmes disposants de caches mémoire." Phd thesis, Université Paris Sud - Paris XI, 2002. http://tel.archives-ouvertes.fr/tel-00695930.
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Ce mémoire présente une nouvelle approche pour le calcul de temps d'exécution au pire (WCET) de tâche temps-réel critique, en particulier en ce qui concerne les aléas dus aux caches mémoire. Le point général est fait sur la problématique et l'état de l'art en la matière, mais l'accent est mis sur la théorie elle-même et son formalisme, d'abord dans le cadre monotâche puis dans le cadre multitâche. La méthode utilisée repose sur une technique d'interprétation abstraite, comme la plupart des autres méthodes de calcul de WCET, mais le formalisme est dans une approche probabiliste (bien que déterministe dans le cadre monotâche) de par l'utilisation de chaînes de Markov. La généralisation au cadre multitâche utilise les propriétés proba- bilistes pour faire une évaluation pessimiste d'un WCET et d'un écart type au pire, grâce à une modification astucieuse du propagateur dans ce cadre. Des premières évaluations du modèle, codées à la main à partir des résultats de compilation d'applications assez simples montrent des résultats promet- teurs quant à l'application du modèle sur des programmes réels en vraie grandeur.
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Jansen, Anthony Robert 1973. "Encoding and parsing of algebraic expressions by experienced users of mathematics." Monash University, School of Computer Science and Software Engineering, 2002. http://arrow.monash.edu.au/hdl/1959.1/8059.
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Buchholz, Peter, and Tuğrul Dayar. "Block SOR Preconditional Projection Methods for Kronecker Structured Markovian Representations." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-100464.
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Hierarchical Markovian Models (HMMs) are composed of multiple low level models (LLMs) and high level model (HLM) that defines the interaction among LLMs. The essence of the HMM approach is to model the system at hand in the form of interacting components so that its (larger) underlying continous-time Markov chain (CTMC) is not generated but implicitly represented as a sum of Kronecker products of (smaller) component matrices. The Kronecker structure of an HMM induces nested block partitionings in its underlying CTMC. These partitionings may be used in block versions of classical iterative methods based on splittings, such as block SOR (BSOR), to solve the underlying CTMC for its stationary vector. Therein the problem becomes that of solving multiple nonsingular linear systems whose coefficient matrices are the diagonal blocks of a particular partitioning. This paper shows that in each HLM state there may be diagonal blocks with identical off-diagonal parts and diagonals differing from each other by a multiple of the identity matrix. Such diagonal blocks are named candidate blocks. The paper explains how candidate blocks can be detected and how the can mutually benefit from a single real Schur factorization. It gives sufficient conditions for the existence of diagonal blocks with real eigenvalues and shows how these conditions can be checked using component matrices. It describes how the sparse real Schur factors of candidate blocks satisfying these conditions can be constructed from component matrices and their real Schur factors. It also demonstrates how fill in- of LU factorized (non-candidate) diagonal blocks can be reduced by using the column approximate minimum degree algorithm (COLAMD). Then it presents a three-level BSOR solver in which the diagonal blocks at the first level are solved using block Gauss-Seidel (BGS) at the second and the methods of real Schur and LU factorizations at the third level. Finally, on a set of numerical experiments it shows how these ideas can be used to reduce the storage required by the factors of the diagonal blocks at the third level and to improve the solution time compared to an all LU factorization implementation of the three-level BSOR solver.
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Buchholz, Peter, and Tuğrul Dayar. "Block SOR Preconditional Projection Methods for Kronecker Structured Markovian Representations." Technische Universität Dresden, 2003. https://tud.qucosa.de/id/qucosa%3A26304.
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Hierarchical Markovian Models (HMMs) are composed of multiple low level models (LLMs) and high level model (HLM) that defines the interaction among LLMs. The essence of the HMM approach is to model the system at hand in the form of interacting components so that its (larger) underlying continous-time Markov chain (CTMC) is not generated but implicitly represented as a sum of Kronecker products of (smaller) component matrices. The Kronecker structure of an HMM induces nested block partitionings in its underlying CTMC. These partitionings may be used in block versions of classical iterative methods based on splittings, such as block SOR (BSOR), to solve the underlying CTMC for its stationary vector. Therein the problem becomes that of solving multiple nonsingular linear systems whose coefficient matrices are the diagonal blocks of a particular partitioning. This paper shows that in each HLM state there may be diagonal blocks with identical off-diagonal parts and diagonals differing from each other by a multiple of the identity matrix. Such diagonal blocks are named candidate blocks. The paper explains how candidate blocks can be detected and how the can mutually benefit from a single real Schur factorization. It gives sufficient conditions for the existence of diagonal blocks with real eigenvalues and shows how these conditions can be checked using component matrices. It describes how the sparse real Schur factors of candidate blocks satisfying these conditions can be constructed from component matrices and their real Schur factors. It also demonstrates how fill in- of LU factorized (non-candidate) diagonal blocks can be reduced by using the column approximate minimum degree algorithm (COLAMD). Then it presents a three-level BSOR solver in which the diagonal blocks at the first level are solved using block Gauss-Seidel (BGS) at the second and the methods of real Schur and LU factorizations at the third level. Finally, on a set of numerical experiments it shows how these ideas can be used to reduce the storage required by the factors of the diagonal blocks at the third level and to improve the solution time compared to an all LU factorization implementation of the three-level BSOR solver.
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Schlüeter, Dirk Christopher. "Universal moduli of parabolic sheaves on stable marked curves." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:b0260f8e-6654-4bec-b670-5e925fd403dd.
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The topic of this thesis is the moduli theory of (parabolic) sheaves on stable curves. Using geometric invariant theory (GIT), universal moduli spaces of semistable parabolic sheaves on stable marked curves are constructed: `universal' indicates that these are moduli spaces of pairs where the underlying marked curve may vary as well as the parabolic sheaf (as in the Pandharipande moduli space for pairs of stable curves and torsion-free sheaves without augmentations). As an intermediate step in this construction, we construct moduli spaces of semistable parabolic sheaves on flat families of arbitrary projective schemes (of any dimension or singularity type): this is the technical core of this thesis. These moduli spaces are projective, since they are constructed as GIT quotients of projective parameter spaces. The stability condition for parabolic sheaves depends on a choice of polarisation and is derived from the Hilbert-Mumford criterion. It is not quite the same as traditional stability with respect to parabolic Hilbert polynomials, but it is closely related to it, and the resulting moduli spaces are always compactifications of moduli of slope-stable parabolic sheaves. The construction works over algebraically closed fields of arbitrary characteristic.
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Weinzierl, Marion [Verfasser], Hans-Joachim [Akademischer Betreuer] Bungartz, Irad [Akademischer Betreuer] Yavneh, and Miriam [Akademischer Betreuer] Mehl. "Hybrid Geometric-Algebraic Matrix-Free Multigrid on Spacetrees / Marion Weinzierl. Gutachter: Hans-Joachim Bungartz ; Irad Yavneh ; Miriam Mehl. Betreuer: Hans-Joachim Bungartz." München : Universitätsbibliothek der TU München, 2013. http://d-nb.info/1038526779/34.
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Trabelsi, Brahim. "Simulation numérique de l’écoulement et mélange granulaires par des éléments discrets ellipsoïdaux." Phd thesis, Toulouse, INPT, 2013. http://oatao.univ-toulouse.fr/9300/1/trabelsi.pdf.
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Les matériaux granulaires sont omniprésents, ils se trouvent aussi bien dans la nature que dans quelques applications industrielles. Parmi les applications industrielles utilisant les matériaux granulaires, on cite le mélange des poudres dans les industries agro-alimentaires, chimiques, métallurgiques et pharmaceutiques. La caractérisation et l'étude du comportement de ces matériaux sont nécessaires pour la compréhension de plusieurs phénomènes naturels comme le mouvement des dunes et les avalanches de neige, et de processus industriels tel que l'écoulement et le mélange des grains dans un mélangeur. Le comportement varié des matériaux granulaires les rend inclassables parmi les trois états de la matière : solide, liquide et gazeux. Ceci a fait dire qu'il s'agit d'un ``quatrième état'' de la matière, situé entre solide et liquide. L'objectif de ce travail est de concevoir et de mettre en oeuvre des méthodes efficaces d'éléments discrets pour la simulation et l'analyse des processus de mélange et de ségrégation des particules ellipsoïdales dans des mélangeurs culbutants industriels tels que le mélangeur à cerceaux. Dans la DEM l'étape la plus critique en terme de temps CPU est celle de la détection et de résolution de contact. Donc pour que la DEM soit efficace il faut optimiser cette étape. On se propose de combiner le modèle du potentiel géométrique et la condition algébrique de contact entre deux ellipsoïdes proposée par Wang et al., pour l'élaboration d'un algorithme efficace de détection de contact externe entre particules ellipsoïdales. Puis de de prouver un résultat théorique et d'élaborer un algorithme pour le contact interne. D'autre part, le couplage DEM-chaîne de Markov permet de diminuer très sensiblement le temps de simulation en déterminant la matrice de transition à partir d'une simulation à courte durée puis en calculant l'état du système à l'aide du modèle de chaîne de Markov. En effet, en utilisant la théorie des matrices strictement positives et en se basant sur le théorème de Perron-Frobenius on peut approximer le nombre de transitions nécessaires pour la convergence vers un état donné.
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Baptista, Alexandra Cristina Ferros dos Santos Nascimento. "Sistemas dinâmicos discretos em álgebras." Doctoral thesis, Universidade de Évora, 2012. http://hdl.handle.net/10174/14751.
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Neste trabalho é feito o estudo de sistemas dinâmicos discretos em álgebras de matrizes.
Este tema é explorado recorrendo a várias ferramentas da álgebra linear, com o objectivo
de tirar partido da estrutura algébrica do espaço.
É estudada a aplicação quadrática matricial, tomando uma matriz como parâmetro,
aliando as propriedades algébricas à teoria das aplicações quadráticas escalares já existente,
no caso real e complexo. São exploradas diversas características da dinâmica, tais como,
a existência de ciclos comutativos e não-comutativos, a sua estabilidade, entre outras.
São estudadas possíveis generalizações para o caso matricial das noções de conjunto de
Mandelbrot e de conjunto de Julia.
Os resultados atingidos são aplicados ao estudo da dinâmica da aplicação quadrática
em diferentes álgebras hipercomplexas.
É explorada a iteração quadrática no conjunto das matrizes estocásticas simétricas; as
conclusões ilustram o comportamento do sistema dinâmico discreto definido no espaço das
cadeias de Markov reversíveis; ABSTRACT: In this work we study discrete dynamical systems in matrix algebras. This subject is
explored using different tools of linear algebra, in order to take advantage of the algebraic
structure of the space.
It is studied the iteration of a quadratic family in the algebra of real matrices, with a
parameter matrix, combining the properties of the algebraic theory with the theory of the
quadratic map in the real and complex cases. Several characteristics of the dynamics are
explored, such as, the existence of commutative and non-commutative cycles, its stability,
among others. Possible generalizations of the Mandelbrot set and Julia set are considered
and studied.
The results obtained are applied to the study of the quadratic dynamic in different
hypercomplex algebras.
Quadratic iteration is explored in the set of symmetric stochastic matrices; the findings
illustrate the behavior of the discrete dynamical system on the space of reversible Markov
chains.
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Zaniboni, Alessia. "Un Modello Stocastico per la Teoria dell'Evoluzione." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2016. http://amslaurea.unibo.it/10077/.
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Il testo contiene nozioni base di probabilità necessarie per introdurre i processi stocastici. Sono trattati infatti nel secondo capitolo i processi Gaussiani, di Markov e di Wiener, l'integrazione stocastica alla Ito, e le equazioni differenziali stocastiche. Nel terzo capitolo viene introdotto il rapporto tra la genetica e la matematica, dove si introduce l'evoluzione la selezione naturale, e altri fattori che portano al cambiamento di una popolazione; vengono anche formulate le leggi basilari per una modellizzazione dell’evoluzione fenotipica. Successivamente si entra più nel dettaglio, e si determina un modello stocastico per le mutazioni, cioè un modello che riesca ad approssimare gli effetti dei fattori di fluttuazione all'interno del processo evolutivo.
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Abo, Robert. "Approches formelles pour l'analyse de la performabilité des systèmes communicants mobiles : Applications aux réseaux de capteurs sans fil." Phd thesis, Conservatoire national des arts et metiers - CNAM, 2011. http://tel.archives-ouvertes.fr/tel-00816392.
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Nous nous intéressons à l'analyse des exigences de performabilité des systèmes communicants mobiles par model checking. Nous modélisons ces systèmes à l'aide d'un formalisme de haut niveau issu du π-calcul, permettant de considérer des comportements stochastiques, temporels, déterministes, ou indéterministes. Cependant, dans le π-calcul, la primitive de communication de base des systèmes est la communication en point-à-point synchrone. Or, les systèmes mobiles, qui utilisent des réseaux sans fil, communiquent essentiellement par diffusion locale. C'est pourquoi, dans un premier temps, nous définissons la communication par diffusion dans le π-calcul, afin de mieux modéliser les systèmes que nous étudions. Nous proposons d'utiliser des versions probabilistes et stochastiques de l'algèbre que nous avons défini, pour permettre des études de performance. Nous en définissons une version temporelle permettant de considérer le temps dans les modèles. Mais l'absence d'outils d'analyse des propriétés sur des modèles spécifiés en une algèbre issue du π-calcul est un obstacle majeur à notre travail. La définition de règles de traduction en langage PRISM, nous permet de traduire nos modèles, en modèles de bas niveau supports du model checking, à savoir des chaînes de Markov à temps discret, à temps continu, des automates temporisés, ou des automates temporisés probabilistes. Nous avons choisi l'outil PRISM car, à notre connaissance, dans sa dernière version, il est le seul outil à supporter les formalismes de bas niveau que nous venons de citer, et ainsi il permet de réaliser des études de performabilité complètes. Cette façon de procéder nous permet de pallier à l'absence d'outils d'analyse pour nos modèles. Par la suite, nous appliquons ces concepts théoriques aux réseaux de capteurs sans fil mobiles.
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Bollon, Jean-Marc. "Etude de différentes politiques de pilotage de systèmes de production." Grenoble INPG, 2001. http://www.theses.fr/2001INPG0029.
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Nous nous sommes intéressés dans cette thèse aux politiques de gestion de production à flux tiré. Après avoir constaté la diversité des politiques existantes (basestocke, kanban, politique hybrides dont kanban étendu et kanban généralisé, pilotage optimal, …), nous avons proposé une formulation unifiée pour décrire leur dynamique. La validité de cette formulation est démontrée, puis nous l’appliquons à la description de plusieurs politiques connues. Un algorithme est donné pour pouvoir appliquer facilement cette formulation à une catégorie très générale de politiques. Cette formulation commune des politiques nous a permis de trouver les identités de fonctionnement qui existaient entre le kanban étendu et le kanban généralisé. En introduisant des coûts de possession et des coûts de non satisfaction des demandes, nous avons aussi effectué une comparaison des coûts de plusieurs politiques sous-optimales, en utilisant à chaque fois la politique optimale et son coût comme référence. La politique optimale est calculée par programmation dynamique. Pour finir nous proposons deux méthodes de calcul exact des probabilités stationnaires dans une ligne de production à deux étages où des politiques à flux tirées très générales sont utilisées. Les distributions obtenues sont utilisées pour calculer les coûts de possession et de non satisfaction des demandes
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Andary, Philippe. "Optimisation d'emplois du temps par recuit simulé. Algorithmique des algèbres de Lie libres." Rouen, 1996. http://www.theses.fr/1996ROUES001.
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Cette thèse est constituée de deux parties totalement indépendantes. La première partie est consacrée à la réalisation d'un logiciel de calcul automatique d'emploi du temps optimal, par la méthode du recuit simulé. Le premier chapitre introduit la théorie probabiliste sous-jacente : les chaînes de Markov hétérogènes. Puis nous donnons les principaux résultats permettant de valider cette méthode. Dans le second chapitre, nous présentons le logiciel qui a été développé en Common Lisp Object System, sur machine Lisp. Nous formalisons tout d'abord le problème des emplois du temps, puis nous décrivons, dans ce cadre, notre adaptation de l'algorithme du recuit simulé. Nous donnons enfin les différentes classes abstraites qui captent les propriétés et comportements des diverses entités du problème, ainsi que les méthodes associées à ces classes d'objets. La deuxième partie de ce travail est une contribution à l'algorithmique dans les algèbres de Lie libres. Le premier chapitre introduit les éléments nécessaires à la compréhension du sujet : mots de Lyndon, factorisation de Lyndon d'un monoïde libre, base de Lyndon d'une algèbre de Lie libre. Nous donnons aussi un moyen de calcul de la multiplicité d'un mot apparaissant dans le développement d'un polynôme de Lie dans l'algèbre associative libre. Dans le second chapitre, nous nous intéressons d'une part à la génération de la base de Lyndon dans l'ordre lexicographique par longueur, et, d'autre part, à la génération d'une classe d'évaluation quelconque des mots de Lyndon. Notre réponse au premier problème est basée sur un algorithme de Duval (1988) que nous adaptons pour notre propos. Nous proposons ensuite un algorithme récursif, basé sur la génération de certaines compositions d'entiers, comme solution au second problème. Pour clore ce chapitre, nous donnons un algorithme de génération des mots de Lyndon maximaux (par rapport à l'ordre lexicographique sur les mots de Lyndon) dans leur classe d'évaluation.
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Miller, Killian. "Algebraic Multigrid for Markov Chains and Tensor Decomposition." Thesis, 2012. http://hdl.handle.net/10012/7234.
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The majority of this thesis is concerned with the development of efficient and robust numerical methods based on adaptive algebraic multigrid to compute the stationary distribution of Markov chains. It is shown that classical algebraic multigrid techniques can be applied in an exact interpolation scheme framework to compute the stationary distribution of irreducible, homogeneous Markov chains. A quantitative analysis shows that algebraically smooth multiplicative error is locally constant along strong connections in a scaled system operator, which suggests that classical algebraic multigrid coarsening and interpolation can be applied to the class of nonsymmetric irreducible singular M-matrices with zero column sums. Acceleration schemes based on fine-level iterant recombination, and over-correction of the coarse-grid correction are developed to improve the rate of convergence and scalability of simple adaptive aggregation multigrid methods for Markov chains. Numerical tests over a wide range of challenging nonsymmetric test problems demonstrate the effectiveness of the proposed multilevel method and the acceleration schemes.
This thesis also investigates the application of adaptive algebraic multigrid techniques for computing the canonical decomposition of higher-order tensors. The canonical decomposition is formulated as a least squares optimization problem, for which local minimizers are computed by solving the first-order optimality equations. The proposed multilevel method consists of two phases: an adaptive setup phase that uses a multiplicative correction scheme in conjunction with bootstrap algebraic multigrid interpolation to build the necessary operators on each level, and a solve phase that uses additive correction cycles based on the full approximation scheme to efficiently obtain an accurate solution. The alternating least squares method, which is a standard one-level iterative method for computing the canonical decomposition, is used as the relaxation scheme. Numerical tests show that for certain test problems arising from the discretization of high-dimensional partial differential equations on regular lattices the proposed multilevel method significantly outperforms the standard alternating least squares method when a high level of accuracy is required.
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Mitsos, Markos [Verfasser]. "[Singuläre Modulformen und involutive Algebren] ; Thema Singuläre Modulformen und involutive Algebren / vorgelegt von Markos Mitsos." 2001. http://d-nb.info/961744979/34.
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Soriano, Solá Marcos [Verfasser]. "Contributions to the integral representation theory of Iwahori-Hecke algebras / vorgelegt von Marcos Soriano Solá." 2002. http://d-nb.info/964312743/34.
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Csenki, Attila. "A differential equation for a class of discrete lifetime distributions with an application in reliability: A demonstration of the utility of computer algebra." 2013. http://hdl.handle.net/10454/11682.
Full textAbstract:
YesIt is shown that the probability generating function of a lifetime random variable T on a finite lattice with polynomial failure rate satisfies a certain differential equation. The interrelationship with Markov chain theory is highlighted. The differential equation gives rise to a system of differential equations which, when inverted, can be used in the limit to express the polynomial coefficients in terms of the factorial moments of T. This then can be used to estimate the polynomial coefficients. Some special cases are worked through symbolically using Computer Algebra. A simulation study is used to validate the approach and to explore its potential in the reliability context.
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Brilman, Matthieu. "Evaluation de performances d'une classe de systemes de ressources partagees." Phd thesis, 1996. http://tel.archives-ouvertes.fr/tel-00004981.
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Nous presentons un modele de systemes de ressources partagees sur lequel nous definissons un parametre de performances fondamental : $\gamma$. Nous cherchons ensuite a etudier ce parametre de performances pour une classe de systemes stochastiques. Apres avoir presente quelques proprietes analytiques de $\gamma$, nous nous interessons a son evaluation. Les calculs exacts etant rarement possibles, nous recherchons des bornes. Plusieurs approches sont presentees. Les resultats mettent en valeur une notion importante : celle de graphe d'exclusion d'un systeme de ressources partagees. En effet, les bornes obtenues sont fonctions de quantites simples definies sur ce graphe, telles que le degre moyen ou le nombre chromatique. Nous montrons ensuite les resultats qu'apportent les bornes que nous avons trouvees pour l'estimation d'exposants de Lyapunov de matrices stochastiques dans l'algebre (max,+).