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Dissertations / Theses on the topic 'Frobenius-Perron theorem'

Author: Grafiati

Published: 24 April 2022

Last updated: 30 July 2025

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1

Lagro, Matthew Patrick. "A Perron-Frobenius Type of Theorem for Quantum Operations." Diss., Temple University Libraries, 2015. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/339694.

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Mathematics<br>Ph.D.<br>Quantum random walks are a generalization of classical Markovian random walks to a quantum mechanical or quantum computing setting. Quantum walks have promising applications but are complicated by quantum decoherence. We prove that the long-time limiting behavior of the class of quantum operations which are the convex combination of norm one operators is governed by the eigenvectors with norm one eigenvalues which are shared by the operators. This class includes all operations formed by a coherent operation with positive probability of orthogonal measurement at each ste

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2

Gautier, Antoine [Verfasser], and Matthias [Akademischer Betreuer] Hein. "Perron-Frobenius theorem for multi-homogeneous mappings with applications to nonnegative tensors / Antoine Gautier ; Betreuer: Matthias Hein." Saarbrücken : Saarländische Universitäts- und Landesbibliothek, 2019. http://d-nb.info/1201647207/34.

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3

Gautier, Antoine Verfasser], and Matthias [Akademischer Betreuer] [Hein. "Perron-Frobenius theorem for multi-homogeneous mappings with applications to nonnegative tensors / Antoine Gautier ; Betreuer: Matthias Hein." Saarbrücken : Saarländische Universitäts- und Landesbibliothek, 2019. http://d-nb.info/1201647207/34.

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4

Vasireddy, Jhansi Lakshmi. "Applications of Linear Algebra to Information Retrieval." Digital Archive @ GSU, 2009. http://digitalarchive.gsu.edu/math_theses/71.

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Some of the theory of nonnegative matrices is first presented. The Perron-Frobenius theorem is highlighted. Some of the important linear algebraic methods of information retrieval are surveyed. Latent Semantic Indexing (LSI), which uses the singular value de-composition is discussed. The Hyper-Text Induced Topic Search (HITS) algorithm is next considered; here the power method for finding dominant eigenvectors is employed. Through the use of a theorem by Sinkohrn and Knopp, a modified HITS method is developed. Lastly, the PageRank algorithm is discussed. Numerical examples and MATLAB programs

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5

Slegers, Wouter. "Spectral Theory for Perron-Frobenius operators." Thesis, Uppsala universitet, Tillämpad matematik och statistik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-396647.

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6

Brillon, Laura. "Matrices de Cartan, bases distinguées et systèmes de Toda." Thesis, Toulouse 3, 2017. http://www.theses.fr/2017TOU30077/document.

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Dans cette thèse, nous nous intéressons à plusieurs aspects des systèmes de racines des algèbres de Lie simples. Dans un premier temps, nous étudions les coordonnées des vecteurs propres des matrices de Cartan. Nous commençons par généraliser les travaux de physiciens qui ont montré que les masses des particules dans la théorie des champs de Toda affine sont égales aux coordonnées du vecteur propre de Perron -- Frobenius de la matrice de Cartan. Puis nous adoptons une approche différente, puisque nous utilisons des résultats de la théorie des singularités pour calculer les coordonnées des vect

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7

Lin, Lijing. "Roots of stochastic matrices and fractional matrix powers." Thesis, University of Manchester, 2011. https://www.research.manchester.ac.uk/portal/en/theses/roots-of-stochastic-matrices-and-fractional-matrix-powers(3f7dbb69-7c22-4fe9-9461-429c25c0db85).html.

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In Markov chain models in finance and healthcare a transition matrix over a certain time interval is needed but only a transition matrix over a longer time interval may be available. The problem arises of determining a stochastic $p$th root of astochastic matrix (the given transition matrix). By exploiting the theory of functions of matrices, we develop results on the existence and characterization of stochastic $p$th roots. Our contributions include characterization of when a real matrix hasa real $p$th root, a classification of $p$th roots of a possibly singular matrix,a sufficient condition

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8

Hochart, Antoine. "Nonlinear Perron-Frobenius theory and mean-payoff zero-sum stochastic games." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLX079/document.

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Les jeux stochastiques à somme nulle possèdent une structure récursive qui s'exprime dans leur opérateur de programmation dynamique, appelé opérateur de Shapley. Ce dernier permet d'étudier le comportement asymptotique de la moyenne des paiements par unité de temps. En particulier, le paiement moyen existe et ne dépend pas de l'état initial si l'équation ergodique - une équation non-linéaire aux valeurs propres faisant intervenir l'opérateur de Shapley - admet une solution. Comprendre sous quelles conditions cette équation admet une solution est un problème central de la théorie de Perron-Frob

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9

Qu, Zheng. "Nonlinear Perron-Frobenius theory and max-plus numerical methods for Hamilton-Jacobi equations." Palaiseau, Ecole polytechnique, 2013. http://pastel.archives-ouvertes.fr/docs/00/92/71/22/PDF/thesis.pdf.

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Une approche fondamentale pour la résolution de problémes de contrôle optimal est basée sur le principe de programmation dynamique. Ce principe conduit aux équations d'Hamilton-Jacobi, qui peuvent être résolues numériquement par des méthodes classiques comme la méthode des différences finies, les méthodes semi-lagrangiennes, ou les schémas antidiffusifs. À cause de la discrétisation de l'espace d'état, la dimension des problèmes de contrôle pouvant être abordés par ces méthodes classiques est souvent limitée à 3 ou 4. Ce phénomène est appellé malédiction de la dimension. Cette thèse porte sur

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10

DEPLANO, DIEGO. "Coordination of multi-agent systems: stability via nonlinear Perron-Frobenius theory and consensus for desynchronization and dynamic estimation." Doctoral thesis, Università degli Studi di Cagliari, 2021. http://hdl.handle.net/11584/310628.

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This thesis addresses a variety of problems that arise in the study of complex networks composed by multiple interacting agents, usually called multi-agent systems (MASs). Each agent is modeled as a dynamical system whose dynamics is fully described by a state-space representation. In the first part the focus is on the application to MASs of recent results that deal with the extensions of Perron-Frobenius theory to nonlinear maps. In the shift from the linear to the nonlinear framework, Perron-Frobenius theory considers maps being order-preserving instead of matrices being nonnegative. The m

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11

Taylor, S. Richard. "Probabilistic Properties of Delay Differential Equations." Thesis, University of Waterloo, 2004. http://hdl.handle.net/10012/1183.

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Systems whose time evolutions are entirely deterministic can nevertheless be studied probabilistically, <em>i. e. </em> in terms of the evolution of probability distributions rather than individual trajectories. This approach is central to the dynamics of ensembles (statistical mechanics) and systems with uncertainty in the initial conditions. It is also the basis of ergodic theory--the study of probabilistic invariants of dynamical systems--which provides one framework for understanding chaotic systems whose time evolutions are erratic and for practical purposes unpredictable.

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12

Kallus, Paul Peter [Verfasser], Etienne [Akademischer Betreuer] Emmich, Karl-Heinz [Akademischer Betreuer] Förster, Jussi [Gutachter] Berndt, and Bela [Gutachter] Nagy. "Semi-monic operator functions : Perron-Frobenius theory, factorization in ordered Banach algebras and degree-reductions / Paul Peter Kallus ; Gutachter: Jussi Berndt, Bela Nagy ; Etienne Emmich, Karl-Heinz Förster." Berlin : Technische Universität Berlin, 2016. http://d-nb.info/1156013046/34.

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13

Fagioli, Marta. "Statistica degli eventi rari nei sistemi dinamici." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2014. http://amslaurea.unibo.it/6942/.

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La teoria dei sistemi dinamici studia l'evoluzione nel tempo dei sistemi fisici e di altra natura. Nonostante la difficoltà di assegnare con esattezza una condizione iniziale (fatto che determina un non-controllo della dinamica del sistema), gli strumenti della teoria ergodica e dello studio dell'evoluzione delle densità di probabilità iniziali dei punti del sistema (operatore di Perron-Frobenius), ci permettono di calcolare la probabilità che un certo evento E (che noi definiamo come evento raro) accada, in particolare la probabilità che il primo tempo in cui E si verifica sia n. Abbiamo stud

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14

Adje, Assalé. "Optimisation et jeux appliqués à l'analyse statique de programmes par interprétation abstraite." Phd thesis, Ecole Polytechnique X, 2011. http://pastel.archives-ouvertes.fr/pastel-00607076.

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L'interprétation abstraite est une méthode générale qui permet de déterminer de manière automatique des invariants de programmes. Cette méthode conduit à résoudre un problème de point fixe non linéaire de grande taille mais qui possède des propriétés de monotonie. Ainsi, déterminer des bornes sur les valeurs prises par une variable au cours de l'exécution d'un programme, est un problème de point fixe équivalent à un problème de jeu à deux joueurs, à somme nulle et avec options d'arrêt. Cette dernière observation explique la mise en oeuvre d'algorithmes d'itérations sur les politiques. Dans un

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15

Adje, Assalé. "Optimisation et jeux appliqués à l'analyse statique de programmes par interprétation abstraite." Phd thesis, Palaiseau, Ecole polytechnique, 2011. https://pastel.hal.science/docs/00/65/10/43/PDF/these.pdf.

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L'interprétation abstraite est une méthode générale qui permet de déterminer de manière automatique des invariants de programmes. Cette méthode conduit à résoudre un problème de point fixe non linéaire de grande taille mais qui possède des propriétés de monotonie. Ainsi, déterminer des bornes sur les valeurs prises par une variable au cours de l'exécution d'un programme, est un problème de point fixe équivalent à un problème de jeu à deux joueurs, à somme nulle et avec options d'arrêt. Cette dernière observation explique la mise en oeuvre d'algorithmes d'itérations sur les politiques. Dans un

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16

LIN, GUAN-YU, and 林冠宇. "Perron-Frobenius theorem and computation on multidimensional arrays." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/h4np99.

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碩士<br>國立高雄大學<br>應用數學系碩博士班<br>106<br>The Perron-Frobenius theorem shows some important results on nonnegative irreducible matrices. This theorem has various applications and extensions. In this paper, we focus on the nonnegative irreducible matrices. After constructing a linear homotopy, we analyze the solution curve of the linear homotopy and prove that any nonnegative irreducible matrix has the positive eigenpair. This is the main result of the Perron-Frobenius theorem. The skill of the proof can be extended to prove the Perron-Frobenius theorem on tensors. Furthermore, the numerical results

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17

Fong, Yi June, and 方儀君. "Perron-Frobenius theorem for sampling operator and the error estimate for its spectral radius formula." Thesis, 1999. http://ndltd.ncl.edu.tw/handle/59359648183021536303.

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18

Hsieh, Li-Yu Shelley. "Ergodic theory of mulitidimensional random dynamical systems." Thesis, 2008. http://hdl.handle.net/1828/1253.

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Given a random dynamical system T constructed from Jablonski transformations, consider its Perron-Frobenius operator P_T. We prove a weak form of the Lasota-Yorke inequality for P_T and thereby prove the existence of BV- invariant densities for T. Using the Spectral Decomposition Theorem we prove that the support of an invariant density is open a.e. and give conditions such that the invariant density for T is unique. We study the asymptotic behavior of the Markov operator P_T, especially when T has a unique absolutely continuous invariant measure (ACIM). Under the assumption of uniquenes

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19

Czenky, Agustina Mercedes. "Sobre las categorías modulares de dimensión impar." Bachelor's thesis, 2019. http://hdl.handle.net/11086/11747.

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Tesis (Lic. en Matemática)--Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía, Física y Computación, 2019.<br>El objetivo de este trabajo es presentar de la manera más autocontenida posible a las categorías modulares de dimensión impar, sus propiedades e invariantes. En la primera parte se exponen las nociones de categorías tensoriales y categorías de fusión. Se presentan construcciones útiles, como la graduación y la equivariantización por grupos finitos, y clases distinguidas de categorías: punteadas, de tipo grupo, nilpotentes, solubles, entre otras. En una segunda parte

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20

Pacheco, Rodríguez Edwin Fernando. "Grafos de Frobenius-Perron para categorías de fusión." Doctoral thesis, 2015. http://hdl.handle.net/11086/2805.

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Tesis (Doctor en Matemática)--Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía y Física, 2015.<br>Sea C una categoría de fusión íntegra, en este trabajo se estudian algunos grafos, llamados el grafo primo y el grafo común divisor, relacionados con las dimensiones de Frobenius-Perron de los objetos simples de C. Estos grafos generalizan los grafos correspondientes asociados a los caracteres irreducibles y a los órdenes de las clases de conjugación en un grupo finito. Se describen los grafos en distintos casos específicos, entre otros, cuando C es una equivariantización bajo l

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21

Lin, Ting-Yu, and 林庭瑀. "Perron-Frobenius Theory and Laplace Transformation for Estimating Parameters and High Order Moments in Multi-state Disease Process." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/wn2znd.

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碩士<br>國立臺灣大學<br>流行病學與預防醫學研究所<br>105<br>Multistate statistical models are often used for dealing with the cardinal questions for infectious disease such as “whether and when the epidemic will occur after the introduction of infectives?” and also for chronic disease such as “how soon the disease will progress from early status to advanced one?”. Both questions are related to two main parameters, basic reproductive number for infectious disease and mean sojourn time for the progression of cancer. However, the derivation of transition kernels are often involved in non-negative matrix and also conv

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22

Soares, Cíntia Dalila. "Évolution dans des populations structurées en classes." Thèse, 2019. http://hdl.handle.net/1866/22666.

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