The aim of this diploma thesis is to cover the catching up with the economic level among the countries of middle and eastern Europe. More accurately it analyses GDP per capita and household income per capita as one of the key economic indicators. The thesis concretely focuses on analysis of beta and sigma convergence and cluster analysis of the mentioned regions and concurrently at the background of the analysis explains some theoretical terms from areas of economics, econometrics and statistics. The analysis was concluded in IBM SPSS programme which belongs to the most complex, user friendly and professionally often used expert tools. The data for the analysis were used from Eurostat.

This diploma thesis deals with the preparation of the two EU Member States, namely Czech Republic and Slovakia, for joining the euro area. The first part briefly describes the formation of the Economic and Monetary Union. The core part lies in the assessment and in the comparison of both states regarding the fulfillment of the criteria for adoption of the single currency. The detailed analysis is focused mostly on the nominal and the real convergence.

This Diploma Paper provides an analysis of the Czech Republic convergence process, which importance grows more in the period before entry into the European Monetary Union. The convergence is evaluated on the basis of three criterion units which are standing alone but fading into each other. It is the Nominal convergence including Maastricht criteria which have been stated in the Treaty on European Union, then Real convergence criteria and criteria which accompany the development of the Optimum Currency Areas Theory. The theoretical part gives the definitions of particular criteria and draw the attention to potential problems which can occur by their interpreting. In the practical part there are comparative characteristics used to analyze achieved state of the convergence in the Czech Republic in relation to EU countries and euro area countries. This part attends also to monitoring the current financial and economical crisis and it's impact on individual indicators.

L'objectif de cette thèse est d'identifier les bases neurales de la représentation de soi chez le primate non-humain, par une approche d'imagerie par résonnance magnétique fonctionnelle. Nous avons pour cela étudié la convergence multimodale 1) à l'échelle de l'aire par la description de la cartographie du sillon intraparietal dans un contexte de stimulations auditives, tactiles et visuelles et 2) à l'échelle du cerveau entier où nous décrivons précisément les sites de convergence visuo-tactile au niveau cortical. Nous avons également étudié le phénomène d'intégration multisensorielle dans un contexte visuo-tactile dynamique, pour lequel nous montrons que les effets comportementaux (étude psychophysique menée chez l'homme) et le réseau d'activations cortical sont maximisés quand le stimulus visuel prédit le stimulus tactile plutôt que lors de leur présentation simultanée. Enfin, nous avons étudié la représentation de l'espace en caractérisant les bases neurales de l'espace proche et de l'espace lointain à partir d'un dispositif expérimental naturaliste et nous montrons l'existence de deux réseaux corticaux qui traitent séparément les informations appartenant à l'espace proche et à l'espace lointain / The aim of this thesis is to investigate the neural basis of self-representation in the non human primate. We studied the multimodal convergence both 1) at the area level precisely mapping auditory, tactile and visual convergence in the intraparietal sulcus and 2) at the whole brain level capturing the spatial pattern of visuo-tactile cortical convergence. We also investigated the neural network subserving multisensory integration in a dynamical visuo tactile context, showing that the strongest behavioral and cortical are obtained when the visual stimuli is predictive of the tactile stimulus rather than during simultaneous presentations. Finally, we studied the representation of space by characterizing the neural bases of near space and far space in a real naturalistic environment, thus providing the neural grounds for the observed behavioral and neuropsychological dissociation between near and far space processing

The aim of the submitted thesis is macroeconomic analysis, comparison and evaluation of nominal and real convergence of the Visegrad Group states with EU-15 states. By the help of regression model, one can state that in years 2004--2008 countries of V4 reached Beta - convergence with EU-15. However, this did not hold for the critical period in 2008--2012 when mainly Hungary lagged behind. There was proved a positive relationship between real and nominal convergence wherewith Balassa-Samuelson Effect for EU states was confirmed. The Czech Republic has always shown a lower nominal value than it would correspond to its GDP per capita, still it approximated to regression line over time. Other V4 states registered inverse course. During period 2004--2012, the Czech Republic performed Maastricht conver-gence criteria best from V4 states. Contrariwise, Hungary had the worst position of the ob-served period.

The aim of the thesis is to analyze the process of nominal and real convergence of the Czech Republic to the average of the European Union (EU-27). The text uses comparison with other european transition economies (Slovakia, Hungary, Poland and Slovenia). The thesis consists of an analysis of the progress of real GDP per capita, comparative price level, labor productivity, employment, labor costs and other indicators. Other topics such as alternative indicators of economical convergence or the accession of the Czech republic into the euro-zone are discussed.

The aim of this thesis is to assess, whether the Czech Republic, Hungary and Poland are ready to adopt the euro. The thesis consists of three main parts. The first part describes the history of the European Monetary Union. The second part focuses on the development of Czech, Hungarian and Polish economy in the years after transformation to a market economy. The last part deals with the Maastricht Convergence Criteria and Real Convergence Criteria, whereas also attempts to assess their actual fulfillment in the Czech Republic, Hungary and Poland.

This Thesis deals with the convergence of European states and identifies the influence of the European union enlargement in 2014 on the course of convergence. Both real and price convergences are analyzed by using beta convergence and sigma convergence concepts. The Balassa Samuelson effect is tested as well. The Balassa Samuelson effect explains the existence of price convergence and also indicates the relationship between real and price variables. The existence of real and price convergence was verified for the whole period from 1995 to 2013. During 2004 the integration of European states was strengthened, which was significant for real convergence because the speed of convergence was positively influenced. As for the price convergence, the year 2004 was insignificant as the break point. Despite a similar course of both convergences, price convergence was more affected by the crisis in 2008. The presence of Balassa Samuelson effect was confirmed. Despite the complications during intensity measurement, caused by problematic dividing into tradable and non tradable sectors, corresponding values are realistic.

Le présent travail se veut une contribution à l’extension du domaine des applications de la théorie des chemins rugueux à travers l’étude de la convergence des processus discrets, qui permet un nouveau regard sur plusieurs problèmes qui se posent dans le cadre du calcul stochastique classique. Nous étudions la convergence en topologie rugueuse, d’abord des chaînes de Markov sur graphes périodiques, ensuite des marches de Markov cachées, et ce changement de cadre permet d’apporter des informations supplémentaires sur la limite grâce à l’anomalie d’aire, invisible en topologie uniforme. Nous voulons montrer que l’utilité de cet objet dépasse le cadre des équations différentielles. Nous montrons également comment le cadre des chemins rugueux permet d’en- coder la manière dont on plonge un modèle discret dans l’espace des fonctions continues, et que les limites des différents plongements peuvent être différenciées précisément grâce à l’anomalie d’aire. Nous définissons ensuite les temps d’occupation itérés pour une chaîne de Markov et montrons, en utilisant les sommes itérées, qu’ils donnent une structure combinatoire aux marches de Markov cachées. Nous proposons une construction des chemins rugueux en passant par les sommes itérées et la comparons à la construction classique, faite par les intégrales itérées, pour trouver à la limite deux types de chemins rugueux différents, non-géométrique et géométrique respectivement. Pour finir, nous illustrons le calcul et la construction de l’anomalie d’aire et nous donnons quelques résultats supplémentaires sur la convergence des sommes et temps d’occupation itérés. / Through the present work, we hope to contribute to extending the domain of applications of rough paths theory by studying the convergence of discrete processes and thus allowing for a new point of view on several issues appearing in the setting of classical stochastic calculus. We study the convergence, first of Markov chains on periodic graphs, then of hidden Markov walks, in rough path topology, and we show that this change of setting allows to bring forward extra information on the limit using the area anomaly, which is invisible in the uniform topology. We want to show that the utility of this object goes beyond the setting of dierential equations. We also show how rough paths can be used to encode the way we embed a discrete process in the space of continuous functions, and that the limits of these embeddings dier precisely by the area anomaly term. We then define the iterated occupation times for a Markov chain and show using iterated sums that they form an underlying combinatorial structure for hidden Markov walks. We then construct rough paths using iterated sums and compare them to the classical construction, which uses iterated integrals, to get two dierent types of rough paths at the limit: the non-geometric and the geometric one respectively. Finally, we illustrate the computation and construction of the area anomaly and we give some extra results on the convergence of iterated sums and occupation times.

Cette thèse est consacrée à l’étude de certains problèmes variationnels de type transition de phase vectorielle ou "phase-field" qui font intervenir une contrainte de divergence. Ces modèles sont généralement basés sur une énergie dépendant d’un paramètre qui peut représenter une grandeur physique négligeable ou qui est liée à une méthode d’approximation numérique par exemple. Une question centrale concerne alors le comportement asymptotique de ces énergies et des minimiseurs globaux ou locaux lorsque ce paramètre tend vers 0. Cette thèse présente différentes stratégies prenant en compte la contrainte de divergence. Elles seront illustrées à travers l’étude de deux modèles. Le premier est une approximation du modèle Eulérien pour le transport branché par un modèle de type phase-field avec divergence prescrite. Nous montrons comment une estimation uniforme de l’énergie, en fonction de la contrainte sur la divergence, permet d’établir un résultat de Gamma-convergence. Le second modèle, en lien avec la théorie du micromagnétisme, concerne des énergies de type Aviles-Giga dans un cadre vectoriel avec contrainte de divergence. Nous illustrerons dans quelle mesure la méthode d’entropie permet de caractériser les minimiseurs globaux. Dans certaines situations nous montrerons une conjecture de type De Giorgi concernant la symétrie 1D des minimiseurs globaux de l’énergie sous une contrainte au bord. / This thesis is devoted to the study of phase-field type variational models with divergence constraint. These models typically involve an energy depending on a parameter which represents a negligible physical quantity or is linked to some numerical approximation method for instance. A central question concerns the asymptotic behavior of these energies and of their global or local minimizers when this parameter goes to 0. We present different strategies which allow to take the divergence constraint into account. They will be illustrated in two models. The first one is a phase-field type approximation, involving a divergence constraint, of the Eulerian model for branched transportation. We illustrate how uniform estimates on the energy, depending on the constraint on the divergence, allow to establish a Gamma-convergence result. The second model, related to micromagnetics, concerns Aviles-Giga type energies for divergence-free vector fields. We use the entropy method in order to characterize global minimizers. In some situations, we will prove a De Giorgi type conjecture concerning the one-dimensional symmetry of global minimizers under boundary conditions.