自從2008年全球經濟衰退以來，歐元區經濟顯著的衰退，特別是歐元區各成員國的經濟表現有明顯的差異。在本文中，我們試就成員國「貿易開放程度」和「財政基本面」這兩個重要特徵，來詮釋歐元區經濟穩定這個議題。在第二章中，我們在貿易開放程度不同的國家下，比較貨幣同盟制度與浮動匯率制度對於負向衝擊產生的影響。我們發現當貨幣當局愈重視產出穩定時，相較於浮動匯率制度，貨幣同盟制度將使產出下降的更多。在第三章中，我們將短期私人債券及長期政府債券引入貨幣同盟的兩國DSGE模型。我們推斷，歐洲央行(ECB)的公共部門債券購買計劃（PSPP），對於不同財政狀況的成員國，有著不對稱的總體經濟影響。在第四章中，我們建立貨幣同盟經濟的最適貨幣政策模型。我們發現成員國間經濟差異，將影響貨幣同盟的整體福利水準。相較於傳統零利率最適貨幣政策文獻，本研究的結果顯示不論是權衡或承諾制度，增加公共部門債券購買將緩和貨幣同盟的經濟波動。 / Since the global recession in 2008, the economic performance of the Euro area has declined significantly. In particular, there have been great differences in the economic performance among member states in the Euro area. In this dissertation, we attempt to address the issue of economic stability by focusing on two key features: the trade openness and the fiscal fundamentals among member states. In Chapter 2, we compare the impacts of the adverse shocks on countries with different degrees of openness under the monetary union regime, and our finding shows that the monetary union will result in a greater decline in output if the monetary authority attaches a higher weight to output stabilization. In Chapter 3, we build a two-country DSGE model representing a monetary union with both short-term and long-term government bonds. We deduce that the ECB’s public sector purchase programme (PSPP) has asymmetric macroeconomic effects on member states under different fiscal fundamentals. In Chapter 4, we set up an optimal monetary policy model of a monetary union. We find that the differences in the economic performance of individual member states will influence the union-wide welfare. Comparing our results with classical literature of optimal monetary policy at zero lower bound, by adding the PSPP, our study indeed reflects lower volatility of the union-wide economy under either discretion or commitment.

L'avènement de l'informatique quantique permet de réétudier les primitives cryptographiques avec une sécurité inconditionnelle, c'est à dire sécurisé même contre des adversaires tout puissants. En 1984, Bennett et Brassard ont construit un protocole quantique de distribution de clé. Dans ce protocole, deux joueurs Alice et Bob coopèrent pour partager une clé secrète inconnue d'une tierce personne Eve. Ce protocole a une sécurité inconditionnelle et n'a pasd'équivalent classique.Dans ma thèse, j'ai étudié les primitives cryptographiques à deux joueurs où ces joueurs ne se font pas confiance. J'étudie principalement le pile ou face quantique et la mise-en-gage quantique de bit. En informatique classique, ces primitivessont réalisables uniquement avec des hypothèses calculatoires, c'est-à-dire en supposant la difficulté d'un problème donné. Des protocoles quantiques ont été construits pour ces primitives où un adversaire peut tricher avec une probabilité constante strictement inférieure à 1, ce qui reste impossible classiquement. Néanmoins, Lo et Chau ont montré l'impossibilité de créer ces primitives parfaitement même en utilisant l'informatique quantique. Il reste donc à déterminer quelles sont les limites physiques de ces primitives.Dans une première partie, je construis un protocole quantique de pile ou face où chaque joueur peut tricher avec probabilité au plus 1/racine(2) + eps pour tout eps > 0. Ce résultat complète un résultat de Kitaev qui dit que dans un jeu de pile ou face quantique, un joueur peut toujours tricher avec probabilité au moins 1/racine(2). J'ai également construit un protocole de mise-en-gage de bit quantique optimal où un joueur peut tricher avec probabilité au plus 0,739 + eps pour tout eps > 0 puis ai montré que ce protocole est en fait optimal. Finalement, j'ai dérivé des bornes inférieures et supérieures pour une autre primitive: la transmission inconsciente, qui est une primitive universelle.Dans une deuxième partie, j'intègre certains aspects pratiques dans ces protocoles. Parfois les appareils de mesure ne donnent aucun résultat, ce sont les pertes dans la mesure. Je construis un protocole de lancer de pièce quantique tolérant aux pertes avec une probabilité de tricher de 0,859. Ensuite, j'étudie le modèle dispositif-indépendant où on ne suppose plus rien sur les appareils de mesure et de création d'état quantique.Finalement, dans une troisième partie, j'étudie ces primitives cryptographiques avec un sécurité computationnelle. En particulier, je fais le lien entre la mise en gage de bit quantique et les protocoles zero-knowledge quantiques. / Quantum computing allows us to revisit the study of quantum cryptographic primitives with information theoretic security. In 1984, Bennett and Brassard presented a protocol of quantum key distribution. In this protocol, Alice and Bob cooperate in order to share a common secret key k, which has to be unknown for a third party that has access to the communication channel. They showed how to perform this task quantumly with an information theoretic security; which is impossible classically.In my thesis, I study cryptographic primitives with two players that do not trust each other. I study mainly coin flipping and bit commitment. Classically, both these primitives are impossible classically with information theoretic security. Quantum protocols for these primitives where constructed where cheating players could cheat with probability stricly smaller than 1. However, Lo, Chau and Mayers showed that these primitives are impossible to achieve perfectly even quantumly if one requires information theoretic security. I study to what extent imperfect protocols can be done in this setting.In the first part, I construct a quantum coin flipping protocol with cheating probabitlity of 1/root(2) + eps for any eps > 0. This completes a result by Kitaev who showed that in any quantum coin flipping protocol, one of the players can cheat with probability at least 1/root(2). I also constructed a quantum bit commitment protocol with cheating probability 0.739 + eps for any eps > 0 and showed that this protocol is essentially optimal. I also derived some upper and lower bounds for quantum oblivious transfer, which is a universal cryptographic primitive.In the second part, I study some practical aspects related to these primitives. I take into account losses than can occur when measuring a quantum state. I construct a Quantum Coin Flipping and Quantum Bit Commitment protocols which are loss-tolerant and have cheating probabilities of 0.859. I also construct these primitives in the device independent model, where the players do not trust their quantum device. Finally, in the third part, I study these cryptographic primitives with information theoretic security. More precisely, I study the relationship between computational quantum bit commitment and quantum zero-knowledge protocols.

This dissertation consists of three research papers dealing with selected issues relevant for central banks after the global financial crisis. The post-crisis world has seen a significant strengthening of the role of central banks with regard to the financial system as well as the real economy. Correspondingly, agendas of some central bankers have grown substantially, encompassing among others monetary policy, financial stability (macro- and microprudential policies) as well as resolution mechanisms. This dissertation thesis reflects the broad focus of some contemporary central banks in three original research articles that concern current unexplored issues for monetary policy and financial stability in the European Union, the Czech Republic, and the United States, potentially bringing policy implications for the relevant authorities. The first article analyzes inflation convergence in the whole European Union (EU) over 1999-2017 and provides comprehensive and robust evidence that the process of inflation convergence among the countries of the EU was not permanently disrupted during the global financial crisis, the European sovereign debt crisis, or the period of zero lower bound interest rates. Specifically, the convergence process did not noticeably weaken after the crisis and the occurrence of...

[pt] Tarifas comerciais podem ser usadas para auxiliar o Banco Central na estabilização da economia? Para responder essa pergunta construímos um modelo Novo Keynesiano de economia aberta com dois países onde as firmas têm poder de mercado suficientemente alto para definir preços diferentes para o mercado local e estrangeiro e obtemos a política monetária e tarifária ótima sob a existência de um limite inferior para a taxa nominal de juros. Fazendo um exercício numérico, analisamos duas situações: quando apenas um país se encontra em uma armadilha de liquidez e quando ambos os países se encontram presos em uma armadilha de liquidez global. Nossos resultados sugerem, que mesmo quando os dois países estão cooperando, a existência do limite inferior da taxa de juros nominal gera uma situação onde o uso ativo de tarifas comerciais pode aumentar o bem-estar da economia. / [en] Can trade tariffs be used to help the Central Bank stabilize the economic cycle? To answer that question we build a New Keynesian Open Economy model with two different countries and where firms have enough market power to set prices in both Home and Foreign markets and calculate the optimal monetary and tariff policy under the existence of a Zero Lower Bound on the nominal interest rate. We perform a numerical exercise to analyse two distinct situations: when only one country is restricted by the Zero Lower Bound and when both countries face this constraint. Our results suggest that the Zero Lower Bound creates a situation in which active use of trade tariffs can be optimal, even if countries are cooperating.

The multiple constant multiplication (MCM) operation is a fundamental operation in digital signal processing (DSP) and digital image processing (DIP). Examples of the MCM are in finite impulse response (FIR) and infinite impulse response (IIR) filters, matrix multiplication, and transforms. The aim of this work is minimizing the complexity of the MCM operation using common subexpression elimination (CSE) technique and redundant number representations. The CSE technique searches and eliminates common digit patterns (subexpressions) among MCM coefficients. More common subexpressions can be found by representing the MCM coefficients using redundant number representations. A CSE algorithm is proposed that works on a type of redundant numbers called the zero-dominant set (ZDS). The ZDS is an extension over the representations of minimum number of non-zero digits called minimum Hamming weight (MHW). Using the ZDS improves CSE algorithms' performance as compared with using the MHW representations. The disadvantage of using the ZDS is it increases the possibility of overlapping patterns (digit collisions). In this case, one or more digits are shared between a number of patterns. Eliminating a pattern results in losing other patterns because of eliminating the common digits. A pattern preservation algorithm (PPA) is developed to resolve the overlapping patterns in the representations. A tree and graph encoders are proposed to generate a larger space of number representations. The algorithms generate redundant representations of a value for a given digit set, radix, and wordlength. The tree encoder is modified to search for common subexpressions simultaneously with generating of the representation tree. A complexity measure is proposed to compare between the subexpressions at each node. The algorithm terminates generating the rest of the representation tree when it finds subexpressions with maximum sharing. This reduces the search space while minimizes the hardware complexity. A combinatoric model of the MCM problem is proposed in this work. The model is obtained by enumerating all the possible solutions of the MCM that resemble a graph called the demand graph. Arc routing on this graph gives the solutions of the MCM problem. A similar arc routing is found in the capacitated arc routing such as the winter salting problem. Ant colony optimization (ACO) meta-heuristics is proposed to traverse the demand graph. The ACO is simulated on a PC using Python programming language. This is to verify the model correctness and the work of the ACO. A parallel simulation of the ACO is carried out on a multi-core super computer using C++ boost graph library.