This thesis presents the modeling of credit risk by using structural approach. Three fundamental questions of credit risk literature are analyzed throughout the research: modeling single firm credit risk, modeling portfolio credit risk and credit risk pricing. First we analyze these questions under the assumptions that firm value follows a geometric Brownian motion and the interest rates are constant. We discuss the weaknesses of the geometric brownian motion assumption in explaining empirical properties of real data. Then we propose a new extended model in which asset value, volatility and interest rates follow affine jump diffusion processes. In our extended model volatility is stochastic, asset value and volatility has correlated jumps and interest rates are stochastic and have jumps. Finally, we analyze the modeling of single firm credit risk and credit risk pricing by using our extended model and show how our model can be used as a solution for the problems we encounter with simple models.

Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / Os Modelos da Onda CinemÃtica e da Onda Difusiva foram aplicados em um rio natural, para estudar a propagaÃÃo de uma onda de cheia neste corpo hÃdrico. Esses modelos sÃo derivaÃÃes do Modelo da Onda DinÃmica, a partir de simplificaÃÃes nas EquaÃÃes de Saint Venant, onde alguns termos sÃo desprezados. No processo de soluÃÃo das equaÃÃes diferenciais, pertinentes aos modelos, foi usado o MÃtodo das DiferenÃas Finitas, sendo que o esquema de aproximaÃÃo explicita foi aplicado para a onda cinemÃtica, enquanto que o esquema de aproximaÃÃo implÃcita foi aplicado para a onda difusiva. Para esta pesquisa, um programa computacional, em linguagem FORTRAN, foi desenvolvido e permitiu que viÃrias simulaÃÃes fossem realizadas, para diferentes cenÃrios encontrados nos rios naturais. Estudos para verificar a sensibilidade dos modelos, com respeito aos parÃmetros hidrÃulicos da bacia, foram realizados. TambÃm foi verificada a influÃncia da linearizaÃÃo das equaÃÃes diferenciais, que compÃem os modelos, nÃs cÃlculos das variÃveis de controle. Os resultados mostraram que o modelo da onda cinemÃtica à mais sensÃvel ao coeficiente de rugosidade das paredes do canal, enquanto que o modelo da onda difusiva à mais sensÃvel para parÃmetros da declividade de fundo do canal, onde este parÃmetro atua diretamente no processo de amortecimento da onda em propagaÃÃo. Os resultados mostraram ainda que, para os cenÃrios usados nas simulaÃÃes, o processo de linearizaÃÃo das equaÃÃes diferenciais nÃo afeta, consideravelmente, a soluÃÃo dos modelos.

In tasks with more than one path to succeed, it is possible that participants’ strategies vary and therefore, participants should not be analyzed as a homogeneous group. This thesis investigates individual differences in a two-dimensional categorization task with redundancy (i.e., a task where any of the two dimensions by itself suffices for perfect performance). Individual differences in learned knowledge and used knowledge are considered and studied. Participants first performed a categorization task with redundancy (training phase), and afterward were asked to do categorizations in which the previously redundant knowledge becomes decisive (testing phase). Using the data from the testing phase, dimension(s) learned by each participant were determined and the response patterns of each participant in the training phase was used to determine which dimension(s) were used. The used knowledge was assessed using two separate analyses, both of which look at accuracy and response time patterns, but in different ways. Analysis 1 uses iterative decision bound modeling and RT-distance hypothesis and Analysis 2 uses the stochastic version of general recognition theory. In Analysis 1, more errors and slower response times close to a decision bound perpendicular to a dimension indicate that a participant is using that dimension. Analysis 2 goes a step further and in addition to determining which dimension(s) are used, specifies in what way they were used (i.e., identifying the strategy of each participant). Possible strategies are described heuristically (unidimensional, time efficient and conservative) and then each heuristic is translated into a drift diffusion model by the unique way that strategy is assumed to affect trial-by-trial difficulty of the task. Finally, a model selection criterion is used to pick the strategy that is used by each participant.

Using deep learning to synthetically generate music is a research domain that has gained more attention from the public in the past few years. A subproblem of music generation is music extension, or the task of taking existing music and extending it. This work proposes the Continuer Pipeline, a novel technique that uses deep learning to take music and extend it in 5 second increments. It does this by treating the musical generation process as an image generation problem; we utilize latent diffusion models (LDMs) to generate spectrograms, which are image representations of music. The Continuer Pipeline is able to receive a waveform as an input, and its output will be what the pipeline predicts the next five seconds might sound like. We trained the Continuer Pipeline using the expansive diffusion model functionality provided by the HuggingFace platform, and our dataset consisted of 256x256 spectrogram images representing 5-second snippets of various hip-hop songs from Spotify. The musical waveforms generated by the Continuer Pipeline are currently at a much lower quality compared to human-generated music, but we affirm that the Continuer Pipeline still has many uses in its current state, and we describe many avenues for future improvement to this technology.

Diffusion Models have achieved state-of-the-art results in image generating tasks, yet face different challenges when used in different domains. We first give a brief overview of the Diffusion Models architecture. Then, we present a new model and architecture called SVGFusion that applies the principles of Diffusion Models to generate Vector Graphics. Vector Graphics have a complex structure and are vastly different than pixel images, and thus the main challenge when working with Vector Graphics is how to represent their complex structure in a way that a Diffusion Model can effectively process. We will explain this and the further challenges that we encountered during the process and how we successfully addressed some of them. We demonstrate the effectiveness of our approach by training a sample model on a decently sized dataset as well as running valuable experiments. Furthermore, we offer useful insights, recommendations and code to researchers who wish to further explore this topic.

The life cycle of Caulobacter crescentus is of interest because of the asymmetric nature of cell division that gives rise to progeny that have distinct morphology and function. One daughter called the stalked cell is sessile and capable of DNA replication, while the second daughter called the swarmer cell is motile but quiescent. Advances in microscopy combined with molecular biology techniques have revealed that macromolecules are localized in a non-homogeneous fashion in the cell cytoplasm, and that dynamic localization of proteins is critical for cell cycle progression and asymmetry. However, the molecular-level mechanisms that govern protein localization, and enable the cell to exploit subcellular localization towards orchestrating an asymmetric life cycle remain obscure. There are also instances of researchers using intuitive reasoning to develop very different verbal explanations of the same biological process. To provide a complementary view of the molecular mechanism controlling the asymmetric division cycle of Caulobacter, we have developed a mathematical model of the cell cycle regulatory network. Our reaction-diffusion models provide additional insight into specific mechanism regulating different aspects of the cell cycle. We describe a molecular mechanism by which the bifunctional histidine kinase PleC exhibits bistable transitions between phosphatase and kinase forms. We demonstrate that the kinase form of PleC is crucial for both swarmer-to-stalked cell morphogenesis, and for replicative asymmetry in the predivisional cell. We propose that localization of the scaffolding protein PopZ can be explained by a Turing-type mechanism. Finally, we discuss a preliminary model of ParA- dependent chromosome segregation. Our model simulations are in agreement with experimentally observed protein distributions in wild-type and mutant cells. In addition to predicting novel mutants that can be tested in the laboratory, we use our models to reconcile competing hypotheses and provide a unified view of the regulatory mechanisms that direct the Caulobacter cell cycle. / Ph. D.

Deep generative models have undergone significant advancements, enabling the production of high-fidelity data across various fields, including computer vision and medical imaging. The availability of paired annotations facilitates a controllable generative process through conditional generative models, which capture the conditional distribution P(X|Y), where X represents high-dimensional data and Y denotes the associated annotation. This controllability makes conditional generative models more preferable than ordinary generative models, which only model P(X). For instance, the latest generative AI techniques within the Artificial Intelligence Generated Content (AIGC) realm have unlocked the potential for flexible image and video generation/editing based on text descriptions or “prompts.” Additionally, generative AI has enhanced model efficiency by supplementing datasets with synthesized data in scenarios where annotations are unavailable or imprecise. Despite these capabilities, challenges persist in ensuring efficient training of conditional generative models. These challenges include: 1) capturing the intricate relationship between data and its annotations, which can introduce biases; 2) higher computational resource requirements during training and inference compared to discriminative models; and 3) the need to balance speed and quality at inference time. To address these challenges, this thesis introduces four models aimed at enhancing the training and inference efficiency of conditional generative models without compromising quality. The first method focuses on conditional Generative Adversarial Networks (cGANs), proposing a novel training objective to improve stability and diversity in synthetic data generation. The second method involves a hybrid generative model that combines GANs and Diffusion-based models to alleviate the unstable training of GANs and accelerate the denoising process. The third model introduces a fine-tuning framework that utilizes pre-trained diffusion parameters for high-fidelity, fast sampling, and quick adaptation during training. The final method presents a super-efficient 3D diffusion model for high-fidelity 3D CT synthesis, addressing the efficiency and quality gap in current models. These methods collectively tackle the efficiency of generative models and enhance generative quality in both computer vision and medical domains, suggesting sustainable solutions for the future of generative AI.

Value-at-Risk (VaR) model fails to predict financial risk accurately especially during financial crises. This is mainly due to the model’s inability to calibrate new market information and the fact that the risk measure is characterised by poor tail risk quantification. An alternative approach which comprises of the Expected Shortfall measure and the Lognormal Jump-Diffusion (LJD) model has been developed to address the aforementioned shortcomings of VaR. This model is called the Simulated-Expected-Shortfall (SES) model. The Maximum Likelihood Estimation (MLE) approach is used in determining the parameters of the LJD model since it’s more reliable and authenticable when compared to other nonconventional parameters estimation approaches mentioned in other literature studies. These parameters are then plugged into the LJD model, which is simulated multiple times in generating the new loss dataset used in the developed model. This SES model is statistically conservative when compared to peers which means it’s more reliable in predicting financial risk especially during a financial crisis. / Statistics / M.Sc. (Statistics)

Nos últimos 60 anos, os modelos de difusão de produtos e de inovações tiveram penetração tão ampla nos mais diversos campos de investigação científica que se tornaram ubíquos, sendo empregados em contextos diversos como no marketing, na Medicina, na Antropologia, na Geografia, por exemplo. Essa abrangência é devido ao papel vital que produtos, inovações e novas tecnologias têm na vida dos indivíduos e no impacto que exercem nas dinâmicas e no desenvolvimento de comunidades, países e de suas economias. Porém, após os grandes saltos dados nas décadas de 1960 e 1970, os estudos em difusão de bens de consumo duráveis deram lugar a pesquisas em sistemas de inovação nas duas décadas seguintes, só voltando a gerar maior interesse acadêmico a partir da década de 2000, com o surgimento dos sistemas de Gestão de Relacionamento com Clientes Customer Relationship Management (CRM) , que tornou disponível um enorme volume de dados; e, também, com o desenvolvimento de novas técnicas de análise, como a modelagem de sistemas complexos. Tendo em vista a carência de estudos integrando modelos de difusão competitiva com modelos de redes usando topologias de redes parcialmente conectadas (small world e livres de escala), este estudo tem como objetivo geral caracterizar a dinâmica da difusão competitiva proposta em redes small world do tipo Watts-Strogatz. Foram realizadas simulações tanto da formulação clássica do modelo de difusão de produtos e de inovações, proposto por Bass (1969), como de proposições mais modernas para difusão competitiva, como os propostos por Libai, Muller e Peres (2009a; 2009b; 2009c) e por Peres, Muller e Mahajan (2010), além de desenvolver um novo modelo incorporando ao de Libai, Muller e Peres (2009c) a topologia de redes de pequeno mundo e outras características de difusão competitiva não presentes na formulação original , permitindo fazer inferências sobre o comportamento da difusão em diversos cenários que não são explicitamente previstos nas formulações clássicas. Por sua lógica intuitiva e simples, o modelo proposto neste trabalho é de valor significativo para o ensino e para a pesquisa da difusão competitiva / In the last 60 years, product and innovation models were so widespread in so many fields of study that they became ubiquitous, being employed in such diverse backgrounds like marketing, medicine, anthropology and geography. Such widespread influence arises from the fact that products, innovations and Technologies have a big role in any individuals daily lives and a huge impact on the development and dynamics of communities, countries and its economies. After huge leaps on this field of research during the 1960s and 1970s, its study faded away from mainstream research in the following two decades. Only regaining widespread academic interest in the beginning of 21st century, with the advent of Customer Relationship Management systems, which made available huge amounts of data, other factors that contributed to this resurgence in diffusion literature were the advancements on new tools for research, notably the developments in complex systems theory and network theory. In the view of the still small, but rapidly increasing, number of studies integrating competitive diffusion and network models of partially connected networks (such as small world networks and scale-free networks), this study aims to characterize the dynamics of competitive diffusion in small world networks with the Watts-Strogatz topology. For its intended purpose, simulations were created, both for the classical formulation of the Bass Diffusion Model, as well as more modern approaches for competitive diffusion, such as the models proposed by Libai, Muller and Peres and Peres, Muller and Mahajan. A new model was developed in order expand the model proposed by Libai et al (2009c) in order incorporate the small world network topology and other characteristics associated to competition that were not explicitly represented. Allowing the inference of behaviors in various scenarios that are not explicitly covered in the classical formulations. For intuitive logic and simplicity, it is believed that this model is of significant value for teaching and for the study of competitive diffusion

Nos últimos 60 anos, os modelos de difusão de produtos e de inovações tiveram penetração tão ampla nos mais diversos campos de investigação científica que se tornaram ubíquos, sendo empregados em contextos diversos como no marketing, na Medicina, na Antropologia, na Geografia, por exemplo. Essa abrangência é devido ao papel vital que produtos, inovações e novas tecnologias têm na vida dos indivíduos e no impacto que exercem nas dinâmicas e no desenvolvimento de comunidades, países e de suas economias. Porém, após os grandes saltos dados nas décadas de 1960 e 1970, os estudos em difusão de bens de consumo duráveis deram lugar a pesquisas em sistemas de inovação nas duas décadas seguintes, só voltando a gerar maior interesse acadêmico a partir da década de 2000, com o surgimento dos sistemas de Gestão de Relacionamento com Clientes Customer Relationship Management (CRM) , que tornou disponível um enorme volume de dados; e, também, com o desenvolvimento de novas técnicas de análise, como a modelagem de sistemas complexos. Tendo em vista a carência de estudos integrando modelos de difusão competitiva com modelos de redes usando topologias de redes parcialmente conectadas (small world e livres de escala), este estudo tem como objetivo geral caracterizar a dinâmica da difusão competitiva proposta em redes small world do tipo Watts-Strogatz. Foram realizadas simulações tanto da formulação clássica do modelo de difusão de produtos e de inovações, proposto por Bass (1969), como de proposições mais modernas para difusão competitiva, como os propostos por Libai, Muller e Peres (2009a; 2009b; 2009c) e por Peres, Muller e Mahajan (2010), além de desenvolver um novo modelo incorporando ao de Libai, Muller e Peres (2009c) a topologia de redes de pequeno mundo e outras características de difusão competitiva não presentes na formulação original , permitindo fazer inferências sobre o comportamento da difusão em diversos cenários que não são explicitamente previstos nas formulações clássicas. Por sua lógica intuitiva e simples, o modelo proposto neste trabalho é de valor significativo para o ensino e para a pesquisa da difusão competitiva / In the last 60 years, product and innovation models were so widespread in so many fields of study that they became ubiquitous, being employed in such diverse backgrounds like marketing, medicine, anthropology and geography. Such widespread influence arises from the fact that products, innovations and Technologies have a big role in any individuals daily lives and a huge impact on the development and dynamics of communities, countries and its economies. After huge leaps on this field of research during the 1960s and 1970s, its study faded away from mainstream research in the following two decades. Only regaining widespread academic interest in the beginning of 21st century, with the advent of Customer Relationship Management systems, which made available huge amounts of data, other factors that contributed to this resurgence in diffusion literature were the advancements on new tools for research, notably the developments in complex systems theory and network theory. In the view of the still small, but rapidly increasing, number of studies integrating competitive diffusion and network models of partially connected networks (such as small world networks and scale-free networks), this study aims to characterize the dynamics of competitive diffusion in small world networks with the Watts-Strogatz topology. For its intended purpose, simulations were created, both for the classical formulation of the Bass Diffusion Model, as well as more modern approaches for competitive diffusion, such as the models proposed by Libai, Muller and Peres and Peres, Muller and Mahajan. A new model was developed in order expand the model proposed by Libai et al (2009c) in order incorporate the small world network topology and other characteristics associated to competition that were not explicitly represented. Allowing the inference of behaviors in various scenarios that are not explicitly covered in the classical formulations. For intuitive logic and simplicity, it is believed that this model is of significant value for teaching and for the study of competitive diffusion