La parité s’est enrichie d’une consolidation en 2013, avec l’abaissement du seuil pour son application aux communes de plus de 1000 habitants. L’étude de la sélection et des carrières des élu-e-s ruraux-ales des années 1970 à 2015, à partir du cas girondin, permet de saisir la manière dont l’espace des activités politiques est investi par les hommes et par les femmes et le rôle qu’y joue la nouvelle contrainte paritaire. À l’aide d’une méthodologie reposant à la fois sur des techniques qualitatives et quantitatives, cette thèse s’efforce de relier les transformations constatées dans la sélection du personnel politique des « petites » communes aux mutations des mondes ruraux contemporains. Elle se veut tout autant une contribution à la sociologie politique des espaces ruraux qu’à la sociologie du genre en politique. / The reform for equal representation of men and women started in 2000s has been consolidated in 2013 by lowering the threshold for an implementation in towns of more than 1’000 inhabitants. The study of political recruitment and political careers of local elected politicians in rural area from 1970 to 2015 in Gironde allows us to understand the political activities of men and women in a context of gender parity which became binding. Using both qualitative and quantitative methods, this dissertation aims to connect the transformation of political recruitment in small towns with the changes of contemporary rural societies. It will thus contribute to the literature in both political sociology of rural societies and gender in politics.

[pt] Desde o século XVI, já existia a idéia de que o poder de compra deveria influenciar no valor de cada moeda. A fim de se entender as relações entre câmbio e inflação, modelos autoregressivos lineares sempre apresentaram dificuldades para superar o passeio aleatório. Possíveis fricções em operações cambiais podem dificultar a arbitragem próxima do câmbio de equilíbrio considerado pelos agentes financeiros. À medida em que se distancia do valor considerado justo, a convergência se torna mais intensa, pois os custos já não seriam uma parcela tão relevante para o lucro potencial da operação. No modelo não-linear proposto, há dois regimes diferentes: um próximo do equilíbrio (comportamento de passeio aleatório) e um comportamento longe dele ocorrendo simultaneamente, mas com pesos variáveis. A depender do nível do câmbio em relação ao equilíbrio, um regime ganha mais peso e outro perde relevância. Essa tese tem o objetivo de avaliar o caráter preditivo do movimento cambiais. O modelo não-linear ESTAR é usado para montar cestas de moedas a serem compradas e vendidas e o retorno advindo de oscilações cambiais é computado. Por fim, incorporamos os efeitos de juros ao modelo para montar portfólios de moedas a fim de simular o retorno de um investimento usando essa estratégia. Para as cestas de moedas, o modelo gerou bons retornos e baixos riscos, tanto em termos de desvio padrão quanto em termos de drawdown. Tal característica foi observada no modelo in-sample e no out-of-sample o que indica um forte caráter preditivo. Levando em conta o efeito dos juros, os portfólios com menos moedas apresentaram retornos positivos, porém essa vantagem é perdida ao se aumentar a quantidade de moedas. / [en] Since the sixteenth century, there was already the idea that purchasing power should influence the value of each currency. In order to understand the relationship between exchange rate and inflation, linear autoregressive models always presented difficulties to beat the random walk. Possible frictions in foreign exchange operations may hinder arbitrage close to the equilibrium exchange rate considered by financial agents. As the exchange rate distances itself from the value considered fair, the convergence becomes more intense, because the costs would no longer be so relevant to the potential profit of the operation. In the proposed nonlinear model, there are two different regimes: one near equilibrium (random walk behavior) and one behavior away from it occurring simultaneously, but with variable weights. For different levels of the exchange rate relative to the equilibrium, one regime gains more weight and the other loses relevance. This thesis aims to evaluate the predictive nature of the exchange rate movement. The nonlinear model ESTAR is used to create baskets of currencies to be bought and sold and the aggregate return based on exchange rate movements is computed. Finally, we consider the interest rate effects on the model to set up currencies portfolios in order to simulate the return on an investment using this strategy. For the baskets of currencies, the model generated good returns and low risks, based on both standard deviation and drawdown. This characteristic was observed in the in-sample model and in the out-of-sample model, which indicates a strong predictive power. Considering the interest effect, portfolios with fewer currencies showed positive returns, but this advantage is lost by increasing the number of currencies.

Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / This work aims to provide non-biased estimates of the speed of reversion of deviations from the PPP for 11 Brazilian cities, between 1991 and 2013, using the methodology proposed by Choi, Mark and Sul (2006), which makes use of a panel estimation method with correction for three possible sources of bias, those being: the bias of inappropriate grouping of cross-section units with heterogeneous coefficients, the Nickell bias and the bias arising from the temporal aggregation of price indexes. The half-lives obtained are of the order of 4.41 and 3.18 years with Brazil and the Average as references, respectively, and median half-life of 3.13 years, when considering all Brazilian cities analyzed as the numeraire. The half-lives found were also substantially lower than those obtained for American cities. Furthermore, 33.33 % of the half-lives obtained were inferior to the consensus range suggested by Rogoff (1996) of 3-5 years, and none surpassed that range. / O presente estudo se propÃe a prover estimativas nÃo viesadas da velocidade de reversÃo dos desvios da PPC para 11 cidades brasileiras entre 1991 e 2013 atravÃs da metodologia proposta por Choi, Mark e Sul (2006) que usam um mÃtodo de estimaÃÃo em painel com correÃÃo para trÃs possÃveis fontes de viÃs, quais sejam, viÃs de agrupamento inapropriado de unidades cross-sections com coeficientes heterogÃneos, viÃs de Nickell e o viÃs oriundo da agregaÃÃo temporal dos Ãndices de preÃos. As meias-vidas obtidas sÃo da ordem de 4.41 e 3.18 anos tendo Brasil e MÃdia como referÃncia, respectivamente, e meia-vida mediana de 3.13 anos considerando todas as cidades brasileiras analisadas como numerÃrio. As meias-vidas encontradas tambÃm se mostraram substancialmente inferiores Ãquelas obtidas para as cidades americanas. AlÃm disso, 33.33% das meias-vidas aqui obtidas se mostraram inferiores ao intervalo consensual proposto por Rogoff (1996) de 3 a 5 anos, e nenhuma o ultrapassou.

nÃo hà / A tese intitulada âTrÃs Ensaios em Macroeconometriaâ à composta de trÃs capÃtulos. O primeiro capÃtulo aplica um modelo em painel dinÃmico para analisar a convergÃncia da taxa de crescimento do PIB per capita, numa abordagem nÃo linear atravÃs de um efeito threshold para os vinte e seis Estados brasileiros mais o Distrito Federal, durante o perÃodo 1985-2005. Os resultados indicam a existÃncia de dois clubes de convergÃncia, um formado pelos estados que se encontram no regime de baixa renda, formado pelos estados da regiÃo nordeste, norte (com exceÃÃo do estado do Amazonas) e o estado de GoiÃs, enquanto que o outro clube à formado por aqueles que se encontram no regime de alta renda, compostos pelos estados da regiÃo sul e sudeste, mais os estados de Mato Grosso, Mato Grosso do Sul e o Distrito Federal. No segundo capÃtulo aplica-se uma formulaÃÃo de tendÃncias comuns Ãs variÃveis PIB real, taxa de juros SELIC nominal, oferta monetÃria do agregado M1 e taxa de inflaÃÃo IPCA, para extrair uma medida de nÃcleo de inflaÃÃo com caracterÃsticas fowardlooking. ApÃs determinar o nÃcleo de inflaÃÃo para o IPCA, testam-se as condiÃÃes para uma medida de nÃcleo segundo Marques et al. (2003) juntamente com duas outras medidas de nÃcleo fornecidas pelo Banco Central do Brasil. Por Ãltimo testam-se a acurÃcia de previsÃes fora da amostra feitas por essas medidas para o IPCA. Os resultados confirmam que a medida de nÃcleo por tendÃncias comuns tem um bom poder preditivo. O terceiro capÃtulo testa a hipÃtese da paridade do poder de compra (PPP) para o Brasil durante o perÃodo de 1985 a 2008 atravÃs da aplicaÃÃo dos testes de raiz unitÃria em painel com dependÃncia transversal apresentados em Moon e Perron (2004) e Pesaran (2007). Utiliza-se como base de dados o Ãndice de inflaÃÃo INPC para nove regiÃes metropolitanas: Belo Horizonte, BelÃm, Curitiba, Fortaleza, Porto Alegre, Recife, Rio de Janeiro, SÃo Paulo e Salvador. Os resultados mostram mudanÃa de persistÃncia apÃs a implementaÃÃo do Plano Real. Enquanto que no perÃodo de alta inflaÃÃo a hipÃtese de Paridade do Poder de Compra PPP à satisfeita, no perÃodo de estabilizaÃÃo de preÃos a PPP nÃo à satisfeita. Este resultado à fortalecido atravÃs da anÃlise das estatÃsticas descritivas dos dados. / The thesis entitled "TrÃs Ensaios em Macroeconometria" is composed of three chapters. The first chapter applies a dynamic panel model to analyze the convergence rate of growth of GDP per capita, non-linear approach using a threshold effect for the twenty-six Brazilian states plus the Distrito Federal during the period 1985-2005. The results indicate the existence of two convergence clubs, one formed by the states that are in the regime of low income, formed by the Northeast region, north (with the exception of the state of Amazonas) and the state of GoiÃs, while other club consists of those who are in the regime of income, formed by the states of South and Southeast, over the states of Mato Grosso, Mato Grosso do Sul and Distrito Federal. The second chapter presents a formulation of common trends in the variables real GDP, nominal interest rate Selic, money supply of M1 and IPCA inflation rate, to extract a measure of core inflation with features foward-looking. After determining the core inflation for the IPCA, we tested the conditions for a measure of core second Marques et al. (2003) along with two other core measures provided by the Banco Central do Brasil. Finally, we tested the accuracy of forecasts out of sample made by these measures to the IPCA. The results confirm that the measure of core inflation by common trends have a good predictive power. The third chapter tests the hypothesis of purchasing power parity (PPP) in Brazil during the period 1985 to 2008 by applying the unit root tests in panel with cross section dependence presented in Moon and Perron (2004) and Pesaran (2007 ). We tested the index of inflation INPC for nine metropolitan areas: Belo Horizonte, BelÃm, Curitiba, Fortaleza, Porto Alegre, Recife, Rio de Janeiro, SÃo Paulo and Salvador. The results show a change in persistence after the Plano Real. While in the period of high inflation the PPP is satisfied, the period of stabilization of prices to PPP is not satisfied. This result is strengthened by examining the descriptive statistics of the data.

Made available in DSpace on 2016-03-15T19:37:38Z (GMT). No. of bitstreams: 1 Mateus Interciso.pdf: 1720671 bytes, checksum: aa67cff2cc9f7abe5fb3b48bead6b38d (MD5) Previous issue date: 2011-08-23 / Fundo Mackenzie de Pesquisa / The search for cellular automata (CAs) rules capable of executing a determined task can be impossible to be achieve manually, given the huge size of the search space usually involved. A method for being able to find rules capable of executing the task at hand has been the usage of genetic algorithms (GAs) to evolve an initially random population, until the desired objective; each individual of those GAs are usually represented by a candidate transition rule. In problems formulated for the resolution by a binary cellular automaton, a recently used modification on the representation of the individuals was the usage of templates with the presence of an extra symbol, capable of representing every other valid symbol. Such schema of ternary representation is used on the present work, aiming for it s net effect on the search process on the GAs. This study is made for two classical tasks of binary unidimensional cellular automata, the density classification task and the parity problem, both traditional in the context of using GAs for searching transition rules with high performance. By comparing the results of the original GAs and their versions implemented with the ternary representation, it s shown that the ternary representation is able to improve the quality of the results. Particularly, it is analized the condition in which the usage of the ternary representation presents to be more effective, as well as some effects of the actual implementation. Possible future works are presented at the end. / A busca por regras de autômatos celulares que efetuem corretamente uma determinada tarefa pode ser impossível de ser efetuada manualmente, dado o enorme tamanho dos espaços de busca usualmente envolvidos. Uma forma para conseguir encontrar boas regras para a execução do problema em questão tem sido a utilização de algoritmos genéticos (AGs) para evoluir uma população inicialmente aleatória, até o objetivo desejado; nesses AGs cada indivíduo é normalmente representado como uma regra de transição candidata. Em problemas formulados para resolução por um autômato celular binário, uma alteração recentemente estudada na literatura para a representação dos indivíduos foi a utilização de templates (moldes) com a presença de um símbolo extra, capaz de representar os demais símbolos. Tal esquema de representação ternária é utilizada no presente trabalho, visando avaliar seu efeito no processo de busca realizado por AGs. O estudo é feito para duas tarefas clássicas de autômatos celulares unidimensionais binários, a tarefa de classificação da densidade e o problema da paridade, ambas tradicionais no contexto da utilização de AGs para encontrar regras de transição com alta performance. Ao comparar os resultados de AGs originais encontrados na literatura com suas versões implementadas com representação ternária, mostra-se que a representação ternária é capaz de melhorar a qualidade dos resultados. Em particular, analisam-se condições em que o uso da representação ternária se mostra mais efetivo, bem como apontam-se efeitos de alguns aspectos de implementação. Possíveis trabalhos futuros pertinentes ao estudo são discutidos ao final.

Made available in DSpace on 2016-03-15T19:37:41Z (GMT). No. of bitstreams: 1 Mateus Interciso.pdf: 1732926 bytes, checksum: f29787f421b0b5f1d6dedd2c1eb4e0fc (MD5) Previous issue date: 2011-09-23 / Fundo Mackenzie de Pesquisa / The search for cellular automata (CAs) rules capable of executing a determined task can be impossible to be achieve manually, given the huge size of the search space usually involved. A method for being able to find rules capable of executing the task at hand has been the usage of genetic algorithms (GAs) to evolve an initially random population, until the desired objective; each individual of those GAs are usually represented by a candidate transition rule. In problems formulated for the resolution by a binary cellular automaton, a recently used modification on the representation of the individuals was the usage of templates with the presence of an extra symbol, capable of representing every other valid symbol. Such schema of ternary representation is used on the present work, aiming for it s net effect on the search process on the GAs. This study is made for two classical tasks of binary unidimensional cellular automata, the density classification task and the parity problem, both traditional in the context of using GAs for searching transition rules with high performance. By comparing the results of the original GAs and their versions implemented with the ternary representation, it s shown that the ternary representation is able to improve the quality of the results. Particularly, it is analized the condition in which the usage of the ternary representation presents to be more effective, as well as some effects of the actual implementation. Possible future works are presented at the end. / A busca por regras de autômatos celulares que efetuem corretamente uma determinada tarefa pode ser impossível de ser efetuada manualmente, dado o enorme tamanho dos espaços de busca usualmente envolvidos. Uma forma para conseguir encontrar boas regras para a execução do problema em questão tem sido a utilização de algoritmos genéticos(AGs) para evoluir uma população inicialmente aleatória, até o objetivo desejado; nesses AGs cada indivíduo é normalmente representado como uma regra de transição candidata. Em problemas formulados para resolução por um autômato celular binário, uma alteração recentemente estudada na literatura para a representação dos indivíduos foi a utilização de templates (moldes) com a presença de um símbolo extra, capaz de representar os demais símbolos. Tal esquema de representação ternária é utilizada no presente trabalho, visando avaliar seu efeito no processo de busca realizado por AGs. O estudo é feito para duas tarefas clássicas de autômatos celulares unidimensionais binários, a tarefa de classificação da densidade e o problema da paridade, ambas tradicionais no contexto da utilização de AGs para encontrar regras de transição com alta performance. Ao comparar os resultados de AGs originais encontrados na literatura com suas versões implementadas com representação ternária, mostra-se que a representação ternária é capaz de melhorar a qualidade dos resultados. Em particular, analisam-se condições em que o uso da representação ternária se mostra mais efetivo, bem como apontam-se efeitos de alguns aspectos de implementação. Possíveis trabalhos futuros pertinentes ao estudo são discutidos ao final.

In this work, we study two problems: first is one of the central problem in learning theory of learning sparse parities and the other k-Vector-SUM is an extension of the not oriousk-SUM problem. We first consider the problem of learning k-parities in the on-line mistake-bound model: given a hidden vector ∈ {0,1}nwith|x|=kand a sequence of “questions” a ,a ,12··· ∈{0,1}n, where the algorithm must reply to each question with〈a ,xi〉(mod 2), what is the best trade off between the number of mistakes made by the algorithm and its time complexity? We improve the previous best result of Buhrman et. al. By an exp (k) factor in the timecomplexity. Next, we consider the problem of learning k-parities in the presence of classification noise of rate η∈(0,12). A polynomial time algorithm for this problem (whenη >0 andk=ω(1))is a longstanding challenge in learning theory. Grigorescu et al. Showed an algorithm running in time(no/2)1+4η2+o(1). Note that this algorithm inherently requires time(nk/2)even when the noise rateη is polynomially small. We observe that for sufficiently small noise rate, it ispossible to break the(nk/2)barrier. In particular, if for some function f(n) =ω(logn) andα∈[12,1),k=n/f(n) andη=o(f(n)−α/logn), then there is an algorithm for the problem with running time poly(n)·( )nk1−α·e−k/4.01.Moving on to the k-Vector-SUM problem, where given n vectors〈v ,v ,...,v12n〉over the vector space Fdq, a target vector tand an integer k>1, determine whether there exists k vectors whose sum list, where sum is over the field Fq. We show a parameterized reduction fromk-Clique problem to k-Vector-SUM problem, thus showing the hardness of k-Vector-SUM. In parameterized complexity theory, our reduction shows that the k-Vector-SUM problem is hard for the class W[1], although, Downey and Fellows have shown the W[1]-hardness result for k-Vector-SUM using other techniques. In our next attempt, we try to show connections between k-Vector-SUM and k-LPN. First we prove that, a variant of k-Vector-SUM problem, called k-Noisy-SUM is at least as hard as the k-LPN problem. This implies that any improvements ink-Noisy-SUM would result into improved algorithms fork-LPN. In our next result, we show a reverse reduction from k-Vector-SUM to k-LPN with high noise rate. Providing lower bounds fork-LPN problem is an open challenge and many algorithms in cryptography have been developed assuming its1 2hardness. Our reduction shows that k-LPN with noise rate η=12−12·nk·2−n(k−1k)cannot be solved in time no(k)assuming Exponential Time Hypothesis and, thus providing lower bound for a weaker version of k-LPN

Les systèmes de régulation des turbomoteurs actuels sont basés sur des architectures complexes que les constructeurs tendent à rendre plus modulaires avec des technologies plus économiques tout en garantissant un niveau de fiabilité supérieur ou égal. Dans ce contexte, la surveillance du circuit carburant, qui a pour but de déceler les dysfonctionnements des composants hydrauliques critiques, permet de réduire le coût de maintenance, d'améliorer le niveau de maintenabilité et d'assurer la disponibilité des turbomoteurs. La présente étude porte sur l'élaboration de méthodes de diagnostic performantes et robustes permettant la détection et la localisation des défauts impactant les fonctions hydrauliques primaires du circuit carburant. Des méthodes existantes de génération de résidus à base de modèles non linéaires sont présentées et appliquées au cas du circuit carburant. L'approche analytique pour le découplage, combinée avec des filtres de Kalman étendus, permet la structuration des résidus pour assurer la localisation des défauts. Une nouvelle approche basée sur la théorie de platitude différentielle est proposée pour le diagnostic de défauts des systèmes non linéaires avec une application au cas du circuit carburant. Les différentiateurs à modes glissants sont utilisés pour l'estimation des dérivées de signaux nécessaires à l'application de certaines méthodes de génération de résidus. Des simulations numériques illustrent la pertinence des résultats obtenus. Une application expérimentale est présentée en utilisant un jeu de données réelles issues d'un banc d'essais partiel et fournies par la société Turbomeca du groupe SAFRAN. / The current gas turbine regulation systems are based on complex architectures that manufacturers tend to make more modular with more cost effective technologies while ensuring a greater or equal level of reliability. In this context, the fuel system health monitoring, which aims to identify critical hydraulic components dysfunction, allows to reduce maintenance costs, to improve maintainability level and to ensure gas turbine availability. The present study focuses on the development of performant and robust diagnosis methods for the detection and isolation of faults affecting primary fuel system hydraulic functions. Existing nonlinear model based residual generation methods are presented and applied to the fuel system. The analytical approach for decoupling, combined with extended Kalman filters, helps fault isolation by generating residual structures. A new approach based on differential flatness theory is proposed for nonlinear systems fault diagnosis with an application to the fuel system. Sliding mode differentiators are used to estimate derived signals that are necessary for the application of some residual generation methods. Numerical simulations illustrate the efficiency of obtained results. An experimental application is presented using a real data set from a partial test bench provided by Turbomeca company of the SAFRAN group.

Objectives. Identify risk factors for at-term small for gestational age newborns. Materials and methods. Retrospective cohort study using data from the Maternal Perinatal Information System of the Maria Auxiliadora Hospital of Lima, from the period 2000-2010. Maternal age, parity, education level, marital status, pregestational body mass index, number of prenatal care visits, presence of conditions such as preeclampsia, eclampsia, urinary tract infection and gestational diabetes as risk factors in small for gestational age newborns were evaluated. The weight for gestational age was calculated based on Peruvian percentiles. Crude relative risk (RR) and adjusted (ARR) were calculated with confidence intervals of 95% using log-binomial generalized linear models. Results. 64,670 pregnant women were included. The incidence for small for gestational age was 7.2%. Preeclampsia (ARR 2.0, 95% CI: 1.86 to 2.15), eclampsia (ARR 3.22, 95% CI: 2.38 to 4.35), low maternal weight (ARR 1.38; 95% CI: 1.23 to 1.54), nulliparity (ARR 1.32, 95% CI: 1.23 to 1.42), age ≥35 years (ARR 1.16, 95% CI: 1.04 -1.29), having prenatal care visits from 0 to 2 (ARR 1.43, 95% CI: 1.32 to 1.55) and 3 to 5 (ARR 1.22, 95% CI: 1.14 to 1.32) were risk factors for small for gestational age. Conclusions. It is necessary to identify pregnant women with risk factors such as those found to decrease the condition of small for gestational age. Actions should emphasize modifiable factors, such as the frequency of prenatal care visits. / Objetivos. Identificar factores de riesgo para neonatos a término pequeños para la edad gestacional. Materiales y métodos. Cohorte retrospectiva que utilizó datos del Sistema Informático Materno Perinatal del Hospital María Auxiliadora de Lima, del período 2000 a 2010. Se evaluó la edad materna, paridad, nivel educativo, estado civil, índice de masa corporal pregestacional, número de controles prenatales, presencia de patologías como preeclampsia, eclampsia, infección urinaria y diabetes gestacional como factores de riesgo en pequeños para edad gestacional. El peso para la edad gestacional fue calculado sobre la base de percentiles peruanos. Se calcularon los riesgos relativos crudos (RR) y ajustados (RRa) con sus intervalos de confianza al 95% usando modelos lineales generalizados log binomial. Resultados. Se incluyeron 64 670 gestantes. La incidencia de pequeños para la edad gestacional fue 7,2%. La preeclampsia (RRa 2,0; IC 95%: 1,86-2,15), eclampsia (RRa 3,22; IC 95%: 2,38-4,35), bajo peso materno (RRa 1,38; IC 95%: 1,23-1,54), nuliparidad (RRa 1,32; IC 95%: 1,23-1,42), edad ≥35 años (RRa 1,16; IC 95%: 1,04-1,29), tener controles prenatales de 0 a 2 (RRa 1,43; IC 95%: 1,32-1,55) y 3 a 5 (RRa 1,22; IC 95%: 1,14-1,32) fueron factores de riesgo para ser pequeños para la edad gestacional. Conclusiones. Es necesario identificar a las gestantes con factores de riesgo como los encontrados para disminuir la condición de pequeños para la edad gestacional. Se debe actuar poniendo énfasis en factores modificables, tales como la frecuencia de sus controles prenatales

The aim of this diploma thesis is based on the empirical analysis to identify the relationship between the exchange rate and the interest rates in selected countries and verify the validity of the uncovered interest rate parity. In the first part, the author deals with basic theoretical and exchange rate determinants from a fundamental analysis point of view, which attempts to explain the causality between these two variables. The actual analysis was performed at three levels on monthly time series from 2010 to 2016. Graphical analysis was selected as the first stage of the analysis, also including verification of the validity of the Fisher International Effect. Later, regression and vector autoregressive analysis followed. However, the conclusions of the individual empirical parts show that the exchange rate is determined by many factors, not only by the interest rate differential, as assumed the theory of uncovered interest rate parity. These results are also related to the low quality of the estimated models. Uncovered interest rate parity has been confirmed in very few cases, but none of the monitored currency pairs has been validated at all three levels of empirical analysis at the same time. The work offers valuable insight into the trend appreciation or depreciation of the exchange rates at the positive interest rate differential in the selected period.