A protein is a biopolymer of amino acids that encodes a particular function. Given that there are 20 amino acids possible at each site, even a short protein of 100 amino acids has $20^{100}$ possible variants, making it unrealistic to evaluate all possible sequences in sequence level space. This search space could be reduced by considering the fact that billions of years of evolution exerting a constant pressure has left us with only a small subset of protein sequences that carry out particular cellular functions. The portion of amino acid space occupied by actual proteins found in nature is therefore much smaller than that which is possible cite{kauffman1993origins}. By examining related proteins that share a conserved function and common evolutionary history (heretofore referred to as protein families), it is possible to identify common motifs that are shared. Examination of these motifs allows us to characterize protein families in greater depth and even generate new ``in silico" proteins that are not found in nature, but exhibit properties of a particular protein family. Using novel deep learning approaches and leveraging the large volume of genomic data that is now available due to high-throughput DNA sequencing, it is now possible to examine protein families in a scale and resolution that has never before been possible. By using this abundance of data to learn high dimensional representations of amino acids sequences, in this work, we show that it is possible to generate novel sequences from a particular protein family. Such a deep sequential model-based approach has great value for bioinformatics and biotechnological applications due to its rapid sampling abilities. / Master of Science / Proteins are one of the most important functional biological elements. These are composed of amino acids which link together to form different shapes which might encode a particular function. These proteins may act independently or might form ``complexes" to have a particular function. Therefore, understanding them is of utmost importance. Due to the fact that there are 20 amino acids even a protein sequence fragment of length 5 can have more than 3 million different combinations. Given, that proteins are generally 1000 amino acids long, looking at all the possibilities is next to impossible. In this work, by leveraging the ``deep learning" paradigm and the vast amount of data available, we try to model these proteins and generate new proteins belonging to a specific ``protein family." This approach has great value for bioinformatics and biotechnological applications due to its rapid sampling abilities.

Esta dissertação apresenta o desenvolvimento, a validação e a aplicação de algoritmos para inferência de conectividade neural em registros de EEG contendo potenciais evento-relacionados (ERP). Os sinais foram caracterizados via modelos auto-regressivos multivariados (MVAR) e empregou-se a coerência parcial direcionada (PDC) no estudo das relações de causalidade entre eles. Certas características dos ERPs, como sua transitoriedade intrínseca e as múltiplas repetições em experimentos, levaram ao desenvolvimento de novos algoritmos, como a estimação de modelos conjuntos a partir de vários segmentos de sinal e um procedimento em janela deslizante capaz de descrever a evolução temporal da estatística dos sinais de interesse. Ademais, mostrou-se a possibilidade de estender os resultados da análise assintótica da estatística da PDC ao caso multi-trecho, tornando possível o estudo de sua significância estatística sem recorrer a procedimentos de reamostragem. Os algoritmos foram validados em exemplos com neural mass models, modelos não-lineares capazes de gerar sinais com características muito semelhantes a sinais de EEG reais, e aplicados a uma base de dados pública contendo resultados de experimentos com ratos. / This dissertation presents the development, validation, and application of algorithms for inferring neural connectivity in EEG signals containing event-related potentials (ERP). The time series were described via multivariate auto-regressive models (MVAR) and partial directed coherence (PDC) was used to study causal relations between them. Certain features of the ERPs, such as their transitory behavior and the existence of multiple trials in an experiment, lead to the development of a new algorithm capable of estimating a joint model from multiple segments and a sliding-window procedure for describing the nonstationarity behavior of the signals of interest. Furthermore, the possibility of extending the asymptotic results for PDC\'s statistics to the multi-trial case was demonstrated, allowing, therefore, the study of its statistical significance without recurring to resampling methods. The algorithms were validated in examples with neural mass models, non-linear models capable of generating signals with features very similar to real EEG recordings, and then applied to a publicly available dataset of experiments in rats.

Esta dissertação apresenta o desenvolvimento, a validação e a aplicação de algoritmos para inferência de conectividade neural em registros de EEG contendo potenciais evento-relacionados (ERP). Os sinais foram caracterizados via modelos auto-regressivos multivariados (MVAR) e empregou-se a coerência parcial direcionada (PDC) no estudo das relações de causalidade entre eles. Certas características dos ERPs, como sua transitoriedade intrínseca e as múltiplas repetições em experimentos, levaram ao desenvolvimento de novos algoritmos, como a estimação de modelos conjuntos a partir de vários segmentos de sinal e um procedimento em janela deslizante capaz de descrever a evolução temporal da estatística dos sinais de interesse. Ademais, mostrou-se a possibilidade de estender os resultados da análise assintótica da estatística da PDC ao caso multi-trecho, tornando possível o estudo de sua significância estatística sem recorrer a procedimentos de reamostragem. Os algoritmos foram validados em exemplos com neural mass models, modelos não-lineares capazes de gerar sinais com características muito semelhantes a sinais de EEG reais, e aplicados a uma base de dados pública contendo resultados de experimentos com ratos. / This dissertation presents the development, validation, and application of algorithms for inferring neural connectivity in EEG signals containing event-related potentials (ERP). The time series were described via multivariate auto-regressive models (MVAR) and partial directed coherence (PDC) was used to study causal relations between them. Certain features of the ERPs, such as their transitory behavior and the existence of multiple trials in an experiment, lead to the development of a new algorithm capable of estimating a joint model from multiple segments and a sliding-window procedure for describing the nonstationarity behavior of the signals of interest. Furthermore, the possibility of extending the asymptotic results for PDC\'s statistics to the multi-trial case was demonstrated, allowing, therefore, the study of its statistical significance without recurring to resampling methods. The algorithms were validated in examples with neural mass models, non-linear models capable of generating signals with features very similar to real EEG recordings, and then applied to a publicly available dataset of experiments in rats.

A necessidade de mitigação dos danos ambientais e preservação do meio ambiente fez com que os países repensassem suas formas de produção e consumo, despontando, dentre outras, a preocupação de estimular a produção e o uso de bens ambientais em detrimento aos convencionais. Diante disso, questões sobre a definição e classificação de bens ambientais emergem nas negociações comerciais e se estendem aos meios acadêmicos, e, mais recentemente, se inserem no âmbito conceitual da Economia Verde. Frente a esse cenário e à evolução da discussão sobre os bens ambientais particularmente na Organização Mundial do Comércio (OMC), é importante debater o papel do Brasil como player nesse mercado. Isto porque o volume de exportação e, principalmente, importação desses bens pelo país é significativo, particularmente para as energias renováveis; e também pelo seu potencial de produção nesse setor, com significativos investimentos previstos para os próximos anos. O objetivo deste trabalho é avaliar a trajetória do saldo comercial brasileiro de energias renováveis, adotando como base a lista proposta pela OCDE para negociação no CTE-SS da OMC, e identificar as variáveis que afetam as importações e exportações desses bens no Brasil. Além disto, pretende-se discutir a questão tarifária para a balança comercial brasileira de bens ambientais, especificamente as energias renováveis. A abordagem metodológica utilizada tem como base Castro e Cavalcanti (1997), e emprega um VEC (Modelo de Autoregressão Vetorial com correção de Erro). O período de análise compreende janeiro de 2005 a dezembro de 2010, utilizando-se dados mensais. Além da análise das estatísticas de comércio internacional, discutiram-se os investimentos e projeções para o setor energético no Brasil e no mundo, com base nos relatórios feitos pela ONU e por consultorias independentes. O Brasil, com exceção do etanol, é um importador líquido de bens ambientais na categoria de energiais renováveis, considerada a lista de bens proposta pela OCDE no CTE-SS, sendo que esta pauta compreende basicamente equipamentos para a produção de energias renováveis. Se se levar em conta os relatórios de expansão da oferta enegética para as próximas décadas, elaboradas pelo Ministério de Minas e Energia, e a própria opção brasileira por depender mais de fontes renováveis, pode-se inferir que a importação desses equipamentos pode aumentar nos próximos anos. Os resultados do modelo proposto apontam que as variáveis explicam pouco mais de 41% dos fluxos comerciais brasileiros de energias renováveis para o modelo de exportação e pouco mais de 35% para o modelo de importação. No modelo de exportação dos bens ambientais, destaca-se o PIB mundial; enquanto o PIB brasileiro se destaca como variável relevante no modelo de importação. Com relação às tarifas, observa-se que a média tarifária incidente sobre os bens exportados pelo Brasil é superior à média tarifária sobre os bens que o Brasil importa, dando destaque à elevada tarifa sobre o etanol. Como principais conclusões observa-se que, primeiro, o Brasil carece em certa medida de uma indústria de equipamentos para produção de energias renováveis que atenda à sua demanda, e que gere capacidade competitiva de exportação. Segundo, as decisões políticas e acordos de redução da emissão de gases de efeito estufa, podem ter influenciado nos resultados do modelo, uma vez que o período proposto para a análise foi marcado por acordos e programas de promoção dos renováveis, tanto no âmbito internacional quanto no nacional. Portanto, para futuros trabalhos de modelagem do comércio de energias renováveis é interessante incorporar variáveis representativas desses acordos. / The need for mitigation of damages and preservation of the environment has led countries to rethink their ways of producing and consuming goods, which in turn, generates concern to encourage the production and use of environmental goods in detriment of conventional ones. Questions about definition and classification of environmental goods emerge in the commercial sector and extend to academic environment and, more recently, to the conceptual framework of the Green Economy. In this scenario and due to discussions over evolution of environmental goods particularly in the World Trade Organization (WTO), it is important to discuss the role of Brazil as a player in this market. This is because the volume of exports and especially imports of these goods throughout the country is significant, particularly for renewable energy. In addition, because Brazil has potential in this sector, with significant investment planned for the upcoming years. The objective of this study is to assess the trajectory of the trade surplus of renewable energy, taking as basis the list proposed by the OECD for negotiation in the CTE-SS WTO, and to identify the variables that affect imports and exports of these goods in Brazil. Moreover, we aim to discuss the issue concerning tariffs to the Brazilian balance of trade in environmental goods, specifically renewable energy. The methodological approach is based on Castro and Cavalcanti (1997), and employs a VEC (vector autoregression model with error correction). The analysis period ranges from January 2005 to December 2010, using monthly data. Besides the analysis of international trade statistics, we discussed the investments and projections for the energy sector in Brazil and abroad, based on reports made by the UN and independent consultants. Brazil, with the exception of ethanol, is a net importer of environmental goods in the category of renewable energy, based on the list of goods proposed by the OECD in the CTE-SS, and this agenda basically comprises equipment for the production of renewable energy. Reports of energy supply expansion for the upcoming decades, prepared by the Ministry of Mines and Energy, and the Brazilian option to rely more on renewable sources allow to infer that imports of such equipment may increase in the upcoming years. The results show that the variables of the proposed model explain just over 41% of Brazilian trade flows of renewable energy for the export model and just over 35% for the import model. The export model of environmental goods highlights the world\'s GDP, while Brazil\'s GDP stands out as a relevant variable in the model import. With regard to tariffs, it is observed that the average tariff, levied on goods exported by Brazil, is higher than the average tariff on goods that Brazil imports, where there is focus on high tariffs on ethanol. The main conclusions are that Brazil lacks a certain extent of industrial equipment for renewable energy production that meets its demands and increases export competitiveness. Second, political decisions and agreements to reduce emissions of greenhouse gases may have influenced the results of the model, since the proposed period of analysis was marked by agreements and programs to promote renewable energy, both internationally and nationally. Therefore, it is interesting to incorporate variables representing these agreements for future work on modeling trade of renewable energy.

A necessidade de mitigação dos danos ambientais e preservação do meio ambiente fez com que os países repensassem suas formas de produção e consumo, despontando, dentre outras, a preocupação de estimular a produção e o uso de bens ambientais em detrimento aos convencionais. Diante disso, questões sobre a definição e classificação de bens ambientais emergem nas negociações comerciais e se estendem aos meios acadêmicos, e, mais recentemente, se inserem no âmbito conceitual da Economia Verde. Frente a esse cenário e à evolução da discussão sobre os bens ambientais particularmente na Organização Mundial do Comércio (OMC), é importante debater o papel do Brasil como player nesse mercado. Isto porque o volume de exportação e, principalmente, importação desses bens pelo país é significativo, particularmente para as energias renováveis; e também pelo seu potencial de produção nesse setor, com significativos investimentos previstos para os próximos anos. O objetivo deste trabalho é avaliar a trajetória do saldo comercial brasileiro de energias renováveis, adotando como base a lista proposta pela OCDE para negociação no CTE-SS da OMC, e identificar as variáveis que afetam as importações e exportações desses bens no Brasil. Além disto, pretende-se discutir a questão tarifária para a balança comercial brasileira de bens ambientais, especificamente as energias renováveis. A abordagem metodológica utilizada tem como base Castro e Cavalcanti (1997), e emprega um VEC (Modelo de Autoregressão Vetorial com correção de Erro). O período de análise compreende janeiro de 2005 a dezembro de 2010, utilizando-se dados mensais. Além da análise das estatísticas de comércio internacional, discutiram-se os investimentos e projeções para o setor energético no Brasil e no mundo, com base nos relatórios feitos pela ONU e por consultorias independentes. O Brasil, com exceção do etanol, é um importador líquido de bens ambientais na categoria de energiais renováveis, considerada a lista de bens proposta pela OCDE no CTE-SS, sendo que esta pauta compreende basicamente equipamentos para a produção de energias renováveis. Se se levar em conta os relatórios de expansão da oferta enegética para as próximas décadas, elaboradas pelo Ministério de Minas e Energia, e a própria opção brasileira por depender mais de fontes renováveis, pode-se inferir que a importação desses equipamentos pode aumentar nos próximos anos. Os resultados do modelo proposto apontam que as variáveis explicam pouco mais de 41% dos fluxos comerciais brasileiros de energias renováveis para o modelo de exportação e pouco mais de 35% para o modelo de importação. No modelo de exportação dos bens ambientais, destaca-se o PIB mundial; enquanto o PIB brasileiro se destaca como variável relevante no modelo de importação. Com relação às tarifas, observa-se que a média tarifária incidente sobre os bens exportados pelo Brasil é superior à média tarifária sobre os bens que o Brasil importa, dando destaque à elevada tarifa sobre o etanol. Como principais conclusões observa-se que, primeiro, o Brasil carece em certa medida de uma indústria de equipamentos para produção de energias renováveis que atenda à sua demanda, e que gere capacidade competitiva de exportação. Segundo, as decisões políticas e acordos de redução da emissão de gases de efeito estufa, podem ter influenciado nos resultados do modelo, uma vez que o período proposto para a análise foi marcado por acordos e programas de promoção dos renováveis, tanto no âmbito internacional quanto no nacional. Portanto, para futuros trabalhos de modelagem do comércio de energias renováveis é interessante incorporar variáveis representativas desses acordos. / The need for mitigation of damages and preservation of the environment has led countries to rethink their ways of producing and consuming goods, which in turn, generates concern to encourage the production and use of environmental goods in detriment of conventional ones. Questions about definition and classification of environmental goods emerge in the commercial sector and extend to academic environment and, more recently, to the conceptual framework of the Green Economy. In this scenario and due to discussions over evolution of environmental goods particularly in the World Trade Organization (WTO), it is important to discuss the role of Brazil as a player in this market. This is because the volume of exports and especially imports of these goods throughout the country is significant, particularly for renewable energy. In addition, because Brazil has potential in this sector, with significant investment planned for the upcoming years. The objective of this study is to assess the trajectory of the trade surplus of renewable energy, taking as basis the list proposed by the OECD for negotiation in the CTE-SS WTO, and to identify the variables that affect imports and exports of these goods in Brazil. Moreover, we aim to discuss the issue concerning tariffs to the Brazilian balance of trade in environmental goods, specifically renewable energy. The methodological approach is based on Castro and Cavalcanti (1997), and employs a VEC (vector autoregression model with error correction). The analysis period ranges from January 2005 to December 2010, using monthly data. Besides the analysis of international trade statistics, we discussed the investments and projections for the energy sector in Brazil and abroad, based on reports made by the UN and independent consultants. Brazil, with the exception of ethanol, is a net importer of environmental goods in the category of renewable energy, based on the list of goods proposed by the OECD in the CTE-SS, and this agenda basically comprises equipment for the production of renewable energy. Reports of energy supply expansion for the upcoming decades, prepared by the Ministry of Mines and Energy, and the Brazilian option to rely more on renewable sources allow to infer that imports of such equipment may increase in the upcoming years. The results show that the variables of the proposed model explain just over 41% of Brazilian trade flows of renewable energy for the export model and just over 35% for the import model. The export model of environmental goods highlights the world\'s GDP, while Brazil\'s GDP stands out as a relevant variable in the model import. With regard to tariffs, it is observed that the average tariff, levied on goods exported by Brazil, is higher than the average tariff on goods that Brazil imports, where there is focus on high tariffs on ethanol. The main conclusions are that Brazil lacks a certain extent of industrial equipment for renewable energy production that meets its demands and increases export competitiveness. Second, political decisions and agreements to reduce emissions of greenhouse gases may have influenced the results of the model, since the proposed period of analysis was marked by agreements and programs to promote renewable energy, both internationally and nationally. Therefore, it is interesting to incorporate variables representing these agreements for future work on modeling trade of renewable energy.

Le premier chapitre consiste en une brève revue de littérature dont les éléments sont repris dans les différentes introductions des études empiriques proposées dans la suite de la thèse. L'objet de cet état des lieux est de fixer le cadre général des analyses macro-économétriques opérées dans la thèse. Ce cadre nous permet d'une part, d'envisager une adéquate intégration des anticipations des agents économiques dans le raisonnement ayant mené aux modèles keynésiens actuels et d'autre part, d'effectuer des estimations des principales versions de la courbe de Phillips introduites dans la littérature macro-économique post-seconde guerre mondiale. Dans cette optique, la thèse est constituée de trois études empiriques. Dans la première de ces études, nous nous plaçons au sein d'un cadre uni-varié et tentons de discriminer entre plusieurs spécifications, proposant différentes caractérisations économétriques de la dynamique du taux d'inflation U.S. Essentiellement, trois types de spécifications, théoriquement associés à trois évolutions possibles du taux d'inflation espéré (anticipé), sont mis à l'épreuve. Les résultats de cette première étude montrent que la dynamique du taux d'inflation peut être pertinemment décrite à l'aide d'un modèle à changements de (trois) régimes markoviens dans les dérives (Intercepts) d'un processus autorégressif (d'ordre deux), soit le modèle MSI(3)-AR(2). La deuxième étude s'opère dans le cadre multi-varié d'une Nouvelle Courbe de Phillips Keynésienne à Inflation tendancielle Positive (NKPC-PI). Au sein de ce cadre, la relation d'arbitrage Inflation/Activité réelle est estimée suivant une procédure en deux étapes. Dans la première, nous identifions des régimes distincts du taux d'inflation U.S. à l'aide d'un modèle à changements de (trois) régimes markoviens dans les dérives d'un processus vectoriel autorégressif (d'ordre deux), soit le modèle MSI(3)-VAR(2). Dans la seconde étape, nous estimons les paramètres structurels de cette économie keynésienne afin d'extraire la courbe de Phillips résultante des changements de régimes initialement identifiés. Les résultats de cette deuxième étude nous amènent à conclure à une non-négligeable instabilité de la courbe de Phillips au cours de la période post-seconde guerre mondiale. La troisième étude se présente comme un prolongement et/ou un approfondissement des deux premières. Aussi, dans sa première partie, nous revenons sur les dynamiques tendancielles individuelles des quatre variables intervenant dans le cadre de modélisation NKPC-PI. Les résultats issus de ces premières estimations en contextes uni-variés montrent que seule la dynamique du taux d'inflation et, dans une moindre mesure, celle du coût marginal réel semble obéir à des changements de régimes. La spécification retenue pour l'inflation est celle de la première étude (MSI(3)-AR(2)), tandis que la dynamique du coût marginal réel pourrait être approchée à l'aide d'un modèle à changements de (deux) régimes dans les dérives d'un processus autorégressif (d'ordre deux), soit le modèle MSI(2)-AR(2). Les dynamiques du taux d'actualisation nominal et du taux de croissance de l'output (les deux autres variables du modèle NKPC-PI) semblent, quant à elles, être assez bien caractérisées par des spécifications linéaires autorégressives à deux retards (AR(2)). Sur la base de ces premiers résultats, nous estimons, dans la deuxième partie de l'étude, la nouvelle courbe de Phillips keynésienne en considérant que les processus générateurs des quatre séries du modèle peuvent répondre à de possibles intégrations fractionnelles. Les résultats de ces dernières estimations montrent que la prise en compte simultanée des changements de régimes et de la longue mémoire dans les dynamiques des variables du modèle apporte certains éclairages sur l'évolution du débat mené autour de la relation d'arbitrage post-seconde guerre mondiale. / This PhD thesis proposes, through her three articles, a macro-econometric framework of integrating, in the most adequate way to our sense, the expectations of the economic agents in the reasoning having led to current New-Keynesian models. Upon this specified frame of analysis, we evaluate the effectiveness of various versions of the Phillips curve introduced into the macroeconomic literature. The first study of this thesis takes place in a univariate context and we seek to determine an econometric model leading to best characterize the U.S inflation rate dynamic. In order to achieve this, three types of specifications, associated with three possible evolutions of the expected rate are considered. The first allows an overall instability of the trend or the expected inflation rate. The second considers an alternative specification in which the expected inflation rate is unstable in periodic segments of the sample. Finally, the last specification allows instability of a "mixed type" in which the trend inflation rate is assumed to be random or subject to a probability schema. The results of our study indicate that this last specification is the one that gives the most adequate characterization of the inflation rate dynamic. The inflation rate then appears generated by a second order autoregressive process with, on the one hand, unchanging lag coefficients and, on the other, an unconditional mean which switch between three global regimes of different frequencies of accession. Based on these first results, we extend the analysis in a multivariate framework. The main topics of the second paper are to challenge the rational nature of the agents expectations and the structural effectiveness of the behaviorally micro-based New Keynesian Phillips Curve with a Positive steady state Inflation (NKPC-PI). We then model the trade-off between the U.S inflation rate and a Unit Labor Cost-based measure of the real activity through Markov Switching - Vectorial AutoRegressive (MS-VAR) specifications. These specifications allow to adequately capturing the rationality in the agents expectations process as they underlie a finite number of expected inflation rate regimes, which highlight the agents adaptive beliefs on the achievements of these regimes. Moreover, the results confirm the structural stability of the NKPC-PI over the inflation rate regimes as its deep parameters seem to be unaffected by the regimes switching (Cogley & Sbordone (2005) and Groen & Mumtaz (2008)). In the third study, we extend the analysis of the Phillips curve trade-off. First, we look at determining econometrics models leading to characterize the dynamics of all the variables underlying the trade-off in univariate contexts. As a result, it appears that an adequate way to characterize the agents expectations regarding the dynamics of these variables is to consider a combination of some fixed levels (regimes) in the variables evolutions with an agents adaptive beliefs notion. Finally, based on the implied expectations values of the variables, we show that the Phillips curve seems to disappear when the impact of the expected inflation rate on its current value converges to its long-term value.