Community is created, developed, and produced by CrossFit as an organization through their website mission statement and visual media, and the community of CrossFitters are able to respond in kind on CrossFit social media. CrossFit culture has become a tour-de-force in the health and fitness industry over recent years, where individuals come together from all walks of life to connect to others through a health and fitness-centric focused community. The high- quality promotional media produced by CrossFit HQ offers a glimpse into what the organization promotes and values, and the official webpage is the main starting point for potential new members to engage with CrossFit as an organization. Likewise, the CrossFit Facebook page offers research into how individuals in the CrossFit community engage with promoted material, as well as how they may shape their identity or understanding as a result. Fantasy theme analysis (FTA) is useful for analyzing the way CrossFitters define their identity through their membership in CrossFit culture. FTA can help explain how both the CrossFit website and Facebook posts present the "CrossFit way of life" as an ideal fitness community and its implications for members. Using symbolic convergence theory (SCT) as a lens, research will utilize fantasy theme rhetorical criticism as the methodology with which these CrossFit artifacts (both Facebook posts and corresponding comments) are analyzed in order to develop a better understanding of the fantasy themes found within the CrossFit community as well as how members develop a sense of shared reality and identity through their membership in the organization. / Master of Arts / Community is created, developed, and produced by CrossFit as an organization through their website mission statement and visual media, and the community of CrossFitters are able to respond in kind on CrossFit social media. CrossFit culture has become a tour-de-force in the health and fitness industry over recent years, where individuals come together from all walks of life to connect to others through a health and fitness-centric focused community. The high-quality promotional media produced by CrossFit HQ offers a glimpse into what the organization promotes and values, and the official webpage is the main starting point for potential new members to engage with CrossFit as an organization. Likewise, the CrossFit Facebook page offers research into how individuals in the CrossFit community engage with promoted material, as well as how they may shape their identity or understanding as a result. Using symbolic convergence theory (SCT) as a lens, research will look at CrossFit website content, Facebook posts, and corresponding content to develop a better understanding of the CrossFit community as well as how members develop a sense of shared reality and identity through their membership in the organization.

CONVERGENCE OF PATHS Within the vast urban fabrics live many threads of paths. These paths weave in, out, diagonal, above and underground forming city blocks that we well know. Events happen when these paths interact. They either weave into each other or separate into many. Sometimes a force or desire within the urban layout is so strong that cuts through the threads and weaves a new path that needs to be discovered. The thorn threads become the manifesto of the desire and the spectacle of event. A place is created. When a singular path reaches a point of convergence with another path, their energy merge and transforms into a moment. There is a desire of purposely converge and communicate these paths into unexpected spatial encounters. At the point of convergence, strangers paths merge into each other blending all together into a spider wed of logical confusion, they briefly loose orientation, change form and ultimately experience an event in common. / Master of Architecture

This thesis poses and solves a distribution free learning problem with consensus that arises in the study of estimation and control strategies for distributed sensor networks. Each node i for i = 1, . . . , n of the sensor network collects independent and identically distributed local measurements {z i} := {z i j}j∈N := {(x i j , yi j )}j∈N ⊆ X × Y := Z that are generated by the probability measure ρ i on Z. Each node i for i = 1, . . . , n of the network constructs a sequence of estimates {f i k }k∈N from its local measurements {z i} and from information functionals whose values are exchanged with other nodes as specified by the communication graph G for the network. The optimal estimate of the distribution free learning problem with consensus is cast as a saddle point problem which characterizes the consensus-constrained optimal estimate. This thesis introduces a two stage learning dynamic wherein local estimation is carried out via local least square approximations based on wavelet constructions and information exchange is associated with the Lagrange multipliers of the saddle point problem. Rates of convergence for the two stage learning dynamic are derived based on certain recent probabilistic bounds derived for wavelet approximation of regressor functions. / Master of Science

The convergence rates for the method of Weinstein and a variant method of Aronszajn known as "truncation including the remainder" are derived in terms of the containment gaps between exact and approximating subspaces, using analytical techniques that arise in part in the convergence analysis of finite element methods for differential eigenvalue problems. An example of a one dimensional Schrodinger operator with a potential is presented which arises in quantum mechanics. Examples using the recent eigenvector-free (EVF) method of Beattie and Goerisch are considered. Since the EVF method uses finite element trial functions as approximating vectors, it produces sparse and well-structured coefficient matrices. For these large-order sparse matrix eigenvalue problems, we adapt a spectral transformation Lanczos algorithm for finding a few wanted eigenvalues. For a few particular examples of vibration in beams and plates, convergence behavior is experimentally evaluated. / Ph. D.

This thesis introduces a new model to the field of social dynamics in which each node in a network moves to the mass center of the opinions in its neighborhood weighted by the changing certainty each node has in its own opinion. An upper bound of O(n) is proved for the number of timesteps until this model reaches a stable state. A second model is also analyzed in which nodes move to the mass center of the opinions of the nodes in their neighborhood unweighted by the certainty those nodes have in their opinions. This second model is shown to have a O(d) time complexity, where d is the diameter of the network, on a tree and is compared with a very similar model presented in 2013 by Frischknecht, Keller, and Wattenhofer who found a lower bound on some networks of Ω(3). 2 / Graduate

Cette thèse est consacrée à l'étude des différents problèmes liés aux structures des cubes , en théorie ergodique et en dynamique topologique. Elle est composée de six chapitres. La présentation générale nous permet de présenter certains résultats généraux en théorie ergodique et dynamique topologique. Ces résultats, qui sont associés d'une certaine façon aux structures des cubes, sont la motivation principale de cette thèse. Nous commençons par les structures de cube introduites en théorie ergodique par Host et Kra (2005) pour prouver la convergence dans $L^2 $ de moyennes ergodiques multiples. Ensuite, nous présentons la notion correspondante en dynamique topologique. Cette théorie, développée par Host, Kra et Maass (2010), offre des outils pour comprendre la structure topologique des systèmes dynamiques topologiques. En dernier lieu, nous présentons les principales implications et extensions dérivées de l'étude de ces structures. Ceci nous permet de motiver les nouveaux objets introduits dans la présente thèse, afin d'expliquer l'objet de notre contribution. Dans le Chapitre 1, nous nous attachons au contexte général en théorie ergodique et dynamique topologique, en mettant l'accent sur l'étude de certains facteurs spéciaux. Les Chapitres 2, 3, 4 et 5 nous permettent de développer les contributions de cette thèse. Chaque chapitre est consacré à un thème particulier et aux questions qui s'y rapportent, en théorie ergodique ou en dynamique topologique, et est associé à un article scientifique. Les structures de cube mentionnées plus haut sont toutes définies pour un espace muni d'une unique transformation. Dans le Chapitre 2, nous introduisons une nouvelle structure de cube liée à l'action de deux transformations S et T qui commutent sur un espace métrique compact X. Nous étudions les propriétés topologiques et dynamiques de cette structure et nous l'utilisons pour caractériser les systèmes qui sont des produits ou des facteurs de produits. Nous présentons également plusieurs applications, comme la construction des facteurs spéciaux. Le Chapitre 3 utilise la nouvelle structure de cube définie dans le Chapitre 2 dans une question de théorie ergodique mesurée. Nous montrons la convergence ponctuelle d'une moyenne cubique dans un système muni deux transformations qui commutent. Dans le Chapitre 4, nous étudions le semigroupe enveloppant d'une classe très importante des systèmes dynamiques, les nilsystèmes. Nous utilisons les structures des cubes pour montrer des liens entre propriétés algébriques du semigroupe enveloppant et les propriétés topologiques et dynamiques du système. En particulier, nous caractérisons les nilsystèmes d'ordre 2 par une propriété portant sur leur semigroupe enveloppant. Dans le Chapitre 5, nous étudions les groupes d'automorphismes des espaces symboliques unidimensionnels et bidimensionnels. Nous considérons en premier lieu des systèmes symboliques de faible complexité et utilisons des facteurs spéciaux, dont certains liés aux structures de cube, pour étudier le groupe de leurs automorphismes. Notre résultat principal indique que, pour un système minimal de complexité sous-linéaire, le groupe d'automorphismes est engendré par l'action du shift et un ensemble fini. Par ailleurs, en utilisant les facteurs associés aux structures de cube introduites dans le Chapitre 2, nous étudions le groupe d'automorphismes d'un système de pavages représentatif. La bibliographie, commune à l'ensemble de la thèse, se trouve en fin document / This thesis is devoted to the study of different problems in ergodic theory and topological dynamics related to og cube structures fg. It consists of six chapters. In the General Presentation we review some general results in ergodic theory and topological dynamics associated in some way to cubes structures which motivates this thesis. We start by the cube structures introduced in ergodic theory by Host and Kra (2005) to prove the convergence in $L^2$ of multiple ergodic averages. Then we present its extension to topological dynamics developed by Host, Kra and Maass (2010), which gives tools to understand the topological structure of topological dynamical systems. Finally we present the main implications and extensions derived of studying these structures, we motivate the new objects introduced in the thesis and sketch out our contributions. In Chapter 1 we give a general background in ergodic theory and topological dynamics given emphasis to the treatment of special factors. % We give basic definitions and describe special factors associated to a From Chapter 2 to Chapter 5 we develop the contributions of this thesis. Each one is devoted to a different topic and related questions, both in ergodic theory and topological dynamics. Each one is associated to a scientific article. In Chapter 2 we introduce a novel cube structure to study the actions of two commuting transformations $S$ and $T$ on a compact metric space $X$. In the same chapter we study the topological and dynamical properties of such structure and we use it to characterize products systems and their factors. We also provide some applications, like the construction of special factors. In the same topic, in Chapter 3 we use the new cube structure to prove the pointwise convergence of a cubic average in a system with two commuting transformations. In Chapter 4, we study the enveloping semigroup of a very important class of dynamical systems, the nilsystems. We use cube structures to show connexions between algebraic properties of the enveloping semigroup and the geometry and dynamics of the system. In particular, we characterize nilsystems of order 2 by its enveloping semigroup. In Chapter 5 we study automorphism groups of one-dimensional and two-dimensional symbolic spaces. First, we consider low complexity symbolic systems and use special factors, some related to the introduced cube structures, to study the group of automorphisms. Our main result states that for minimal systems with sublinear complexity such groups are spanned by the shift action and a finite set. Also, using factors associated to the cube structures introduced in Chapter 2 we study the automorphism group of a representative tiling system. The bibliography is defer to the end of this document

La carotte KZai02, forée dans le cône détritique sous-marin du fleuve Zaire/Congo, renseigne du stade isotopique 6.6 à l’Actuel (derniers 165 ka). La dynamique de la végétation de l’Afrique Centrale a été reconstruite sur la base de l’étude de son contenu pollinique. Ces résultats, comparés à ceux du contenu en carbone organique total et au rapport Ti/K, renseignent respectivement sur l’activité des alizés et l’intensité de la mousson dans le passé. Les glaciaires sont caractérisées par des températures basses empêchant le développement de la forêt tropicale humide sur le bassin versant du Zaïre/Congo au bénéfice des savanes. Les interglaciaires sont marquées par le développement de la forêt tropicale humide et des marais de mangrove sur la côte suite à l’élévation du niveau marin. Le passage progressif de zones herbeuses à des environnements plus forestiers témoigne d’un décalage entre les augmentations de température et d’humidité. Le stade isotopique 5 montre deux événements moins chauds (sous-stades 5b et 5d) avec le développement des forêts afromontagnardes (principalement Podocarpus). L’excentricité, l’obliquité et particulièrement la précession ont été identifiées comme ayant exercé une influence sur les écosystèmes végétaux. Ces périodicités ont été interprétées en termes de variations des précipitations liées à des fluctuations de l’ITCZ. Des cycles infra-Milankovitch ont aussi été révélés par l’analyse spectrale. Ils sont attribués (1) aux pulsations glaciaires des événements de Heinrich et de Dansgaard/Oeschger et (2) à des variations à haute fréquence semblables à celles décelées sur la mousson est-asiatique et reliées au contrôle des calottes polaires / Core KZai02 from the Zaire/Congo deep sea fan runs from MIS 6.6 to Present (last 1685 ka). Its pollen study allows to reconstruct the vegetation past variations over the Central Africa. These results, compared to the Total Organic Carbon content (TOC) and the Ti/K ratio, inform on the past trade winds and West African monsoon variability, respectively. During glacials, low temperatures over the Zaire/Congo watershed prevented the development of the tropical rain forest in opposition to savannah. Each interglacial starts with the development of mangrove testifying to events of sea-level rise. Then, the succession of grassy and forested environments indicates a gap between temperature and humidity rises. During the warmer episodes, rain forest expanded over the Central Africa. The Marine Isotope Stage 5 includes two cooler events supported by expansion of the afromontane forest (mainly Podocarpus) corresponding to substages 5b and 5d. Eccentricity, obliquity and particularly precession are identified in variations of the ecological groups of the KZai 02 pollen record and interpreted in terms of variations of precipitations linked to fluctuations of the ITCZ. Sub-Milankovitch periods are also revealed by spectral analysis and related to (1) the Heinrich and Dansgaard/Oeschger glacial pulsation events and (2) high frequency variations similar to the East Asian monsoon oscillations controlled by ice sheets

This thesis concentrates on the new member states of the European Union and their convergent processes. It is particularly focused on five Central European countries -- the Czech Republic, Hungary, Poland, Slovakia and Slovenia, which became the members of the European Union on 1st May 2004. The first chapter deals with the countries during their preparation process for the membership in the EU, the meeting the Copenhagen Criteria and their economic development. The second chapter is focused on the development of Central European countries in the EU. There is featured the development in the first years of their membership and during the economic crisis and the recovery. The third chapter concentrates on the processes of the real and nominal convergence in the Central Europe. Besides monitoring various stages of convergence over time there is documented the course of the convergence by the calculation of beta convergence in the European Union. At the end of the thesis there is outlined the relationship between the degree of nominal and real convergence in the concerned countries.

A Produtividade Total dos Fatores da agropecuária brasileira cresceu a uma taxa média de 2,2% ao ano entre 1975 e 2006, entretanto esse crescimento não ocorreu de forma homogênea entre os estados que compõem o país. Enquanto alguns estados além de terem taxas consistentes de crescimento, por vezes acima da média nacional, outros tiveram um trajetória que oscilava entre momentos de crescimento e estagnação. Tendo em vista essas diferenças na trajetória estadual da produtividade, o objetivo do trabalho é compreender a dinâmica do crescimento da PTF agropecuária brasileira e testar a hipótese das convergências sigma e beta - absoluta e condicional - a um nível geográfico interestadual entre os anos censitários de 1975 e 2006. Para atingir tal objetivo foi utilizado um modelo de regressão linear simples, para o teste da convergência sigma, e um modelo de dados em painel para os casos da convergência beta. Os resultados obtidos não identificaram convergência sigma, indicando um aumento da dispersão da produtividade interestadual, mas há evidências de convergência beta, tanto absoluta quanto condicional, sendo que o tempo de meia-vida para convergência variou entre 168 anos, no caso absoluto, e 172 anos, no caso condicional. A partir dos resultados argumenta-se que o longo período temporal necessário para a convergência beta não consegue ser compreendido sem que se leve em consideração o aumento da dispersão do nível da PTF, evidenciada pela não convergência sigma, pela própria dinâmica da produtividade interestadual e por fatores exógenos, como a condução da política agrícola durante o período em análise. / Brazilian farming total factor productivity grew at an average rate of 2.2% per year from 1975 to 2006, however this growth did not occur in a homogeneous way among the states. While some states besides having consistent rates of growth, sometimes above the national average, others had a trajectory that oscillated between moments of growth and stagnation. In view of these differences in the state productivity trajectory, the objective of this work is to understand the dynamics of the growth of Brazilian agricultural TFP and testing the hypothesis of sigma and beta - absolute and conditional - convergences at a geographical interstate level between. To achieve this objective, a simple linear regression model was used for the sigma convergence test and a panel data model for the cases of beta convergence. The results obtained did not identify sigma convergence, indicating an increase in the dispersion of interstate productivity, but there is evidence of beta convergence, both absolute and conditional, and the half-life for convergence varied between 168 years in the absolute case and 172 years, in the conditional case. From the results it is argued that the long time period required for the beta convergence can\'t be understood without taking into account the increased dispersion of the TFP level, evidenced by sigma non convergence, by the interstate productivity dynamics itself and by exogenous factors such as the conduct of agricultural policy during the period under review.

Le problème du transport optimal, originellement introduit par Monge au 18ème siècle, consiste à minimiser l'énergie nécessaire au déplacement d'une masse dont la répartition est donnée vers une autre masse dont la répartition est elle aussi donnée; mathématiquement, cela se traduit par : trouver le minimiseur de l'intégrale de c(x,T(x)) (où c est le coût de transport de x vers T(x)) parmi toutes les applications T à mesure image prescrite.Cette thèse est consacrée à l'étude de problèmes variationnels similaires où l'on fait intervenir la matrice jacobienne de la fonction de transport, c'est-à-dire que le coût dépend de trois variables c(x,T(x),DT(x)) ; il s'agit typiquement de rajouter l'intégale de |DT(x)|^2 à la fonctionnelle afin d'obtenir une pénalisation Sobolev. Ce type de problème trouve ses motivations en mécanique des milieux continus, élasticité incompressible ou en analyse de forme et appelle d'un point de vue mathématique une approche totalement différente de celle du problème de transport usuel.Les questions suivantes sont envisagées :- bonne définition du problème, notamment de l'énergie de Dirichlet, via les espaces de Sobolev par rapport à une mesure, et résultats d'existence de minimiseurs ;- caractérisation de ces minimiseurs : optimalité du transport croissant sur la droite réelle, et approche du type équation d'Euler-Lagrange en dimension quelconque ;- sélection d'un minimiseur via une procédure de pénalisation du type Gamma-convergence (l'énergie de Dirichlet est mutipliée par un petit paramètre) lorsque le coût de transport est le coût de Monge donné par la distance, pour lequel l'application de transport optimale n'est pas unique ;- autres approches du problème et perspectives : formulation dynamique du type Benamou-Brenier, et formulation duale similaire à celle de Kantorovitch dans le cas du problème du transport optimal usuel. / The optimal transportation problem was originally introduced by Monge in the 18th century; it consists in minimizing the total energy of the displacement of a given repartition of mass onto another given repartition of mass. This is mathematically expressed by: find the minimizer of the integral of c(x,T(x)) (where c(x,T(x)) is the cost to send x onto T(x)) among the maps T with prescribed image measure.This thesis is devoted to similar variational problems, which involve the Jacobian matrix of the transport map, meaning that the cost depends on three variables c(x,T(x),DT(x)); we typically add the Dirichlet energy to the transport functional in view to obtain a Sobolev-type penalization. This kind of constraints finds its motivations in continuum mechanics, incompressible elasticity or shape analysis, and a quite different mathematical approach than in the usual theory of optimal transportation is needed.We consider the following questions:- proper definition of the problem, in particular of the Dirichlet energy, thanks to the theory of Sobolev spaces with respect to a measure, and existence results;- characterizations of these minimizers: optimality of the monotone transport map on the real line, and Euler-Lagrange-like approach in any dimension;- selection of a minimizer via a Gamma-convergence-like penalization procedure (we multiply the Dirihlet energy with a vanishing positive parameter) where the transport cost is the Monge cost given by the distance (for which the optimal transport map is not unique);- other related problems and perspectives: dynamic Benamou-Brenier-like formulation, and dual Kantorovich-like formulation.