Complex systems in biology, climatology, medicine, and economy hold emergent properties such as non-linearity, adaptation, and self-organization. These emergent attributes can derive from large-scale relationships, connections, and interactive behavior despite not being apparent from their isolated components. It is possible to better comprehend complex systems by analyzing cross-correlations between time series. However, the accumulation of non-linear processes induces multiscale structures, therefore, a spectrum of power-law exponents (the fractal dimension) and distinct cyclical patterns. We propose the Multifractal detrended cross-correlation heatmaps (MF-DCCHM) based on the DCCA cross-correlation coefficients with sliding boxes, a systematic approach capable of mapping the relationships between fluctuations of signals on different scales and regimes. The MF-DCCHM uses the integrated series of magnitudes, sliding boxes with sizes of up to 5% of the entire series, and an average of DCCA coefficients on top of the heatmaps for the local analysis. The heatmaps have shown the same cyclical frequencies from the spectral analysis across different multifractal regimes. Our dataset is composed of sales and inventory from the Brazilian automotive sector and macroeconomic descriptors, namely the Gross Domestic Product (GDP) per capita, Nominal Exchange Rate (NER), and the Nominal Interest Rate (NIR) from the Central Bank of Brazil. Our results indicate cross-correlated patterns that can be directly compared with the power-law spectra for multiple regimes. We have also identified cyclical patterns of high intensities that coincide with the Brazilian presidential elections. The MF-DCCHM uncovers non-explicit cyclic patterns, quantifies the relations of two non-stationary signals (noise effect removed), and has outstanding potential for mapping cross-regime patterns in multiple domains.

AgradecimentosCito aqui as pessoas que me ajudaram não só nesta fase, mas ao longo da minha vida. Algumas delas se enquadram em mais de uma categoria.A Nilton e Maria da Conceição Rodrigues, meus pilares, exemplos e referencias, Camila e Pedro Henrique Rodrigues, meus amores e desafetos. Se posso dizer que sou algo hoje, devo muito a vocês. Muito obrigado, minha amada família.A José Guilherme Chauí Berlinck, pelo apoio, conversas, broncas e fanfarronices com as quais você se divertiu às minhas custas ao longo do tempo que trabalhamos juntos. Dei a sorte de ter ao longo do mestrado não um orientador, mas um amigo.A Breno Teixeira Santos, pela "hospedagem" das parasitadas, pela imensa ajuda e pelo que me ensinou.A José Eduardo Soubhia Natali, por toda a ajuda, convivencia ao longo destes anos desde a graduação, por termos a oportunidade de trabalharmos em projetos que puderam dialogar muito. Mas não pelo World of Warcraft. A Fernando Silveira Marques, Ricardo Martins e Talita de Cássia GlinganiSebrian, do laboratório de Fisiologia Teórica, pelo companheirismo e inestimável ajuda, ao longo do mestrado.A Gustavo Kanedo, pelo empréstimo de equipamentos, ajuda na coleta e por me apresentar a Boracéia. Sem dúvida uma grande contribuição para que este processo pudesse se concluir. Ao pessoal do Laboratório de Herpetologia do Departamento de Fisiologia daUniversidade de São Paulo, por toda a ajuda, empréstimo de equipamentos, pitacos, conversas, seminários e pela excelente compania no departamento.Aos professores Luis Henrique Alves Monteiro, Carlos Navas, Silvia Cristina Ribeiro de Souza, pelos indispensáveis comentários a respeito do projeto na qualificação, seminários, e conversas no corredor do departamento. 10A Daniel Daminelli e Rafael Nora Tannus, por tantas discussões, elocubrações, exposições de ideias, confusões, iluminações tortuosas, mas devo um agradecimento especial para uma certa conversa num barzinho da Vila Madalena. Você entrou na minha vida na parte final deste processo, mas teve um papel fundamental. Me apoiou quando cambaleei, me enxergou quando eu precisei ser visto, me compreendeu quando eu mesmo ja não me entendia, e me fez acreditar no que eu já não acreditava mais. "You walk beside me." Amo você.

ABSTRACT. The growing global demand for hydrocarbons has tested the limits of oil exploration and exploitation technologies. Among the seismic methods, tomography is an alternative means for high-resolution characterization of reservoirs, and it enables a more efficient...Keywords: reservoir characterization, traveltime tomography, seismic inversion, regularization, Recôncavo Basin. RESUMO. A crescente demanda mundial por hidrocarbonetos tem testado os limites das tecnologias de exploração e explotação de petróleo. Dentro dos métodos sísmicos, a tomografia surge como alternativa de caracterização de alta resolução dos reservatórios,...Palavras-chave: caracterização de reservatórios, tomografia de tempos de trânsito, inversão s´ísmica, regularização, Bacia do Recôncavo.

Complex systems in biology, climatology, medicine, and economy hold emergent properties such as non-linearity, adaptation, and self-organization. These emergent attributes can derive from large-scale relationships, connections, and interactive behavior despite not being apparent from their isolated components. It is possible to better comprehend complex systems by analyzing cross-correlations between time series. However, the accumulation of non-linear processes induces multiscale structures, therefore, a spectrum of power-law exponents (the fractal dimension) and distinct cyclical patterns. We propose the Multifractal Detrended Cross-Correlation Heatmaps (MF-DCCHM), a systematic approach representing a process with clear, defined, and repeatable steps to map the relationships between fluctuations of signals on different time scales and regimes. Our dataset is composed of sales and inventory from the Brazilian automotive sector and macroeconomic descriptors, namely the Gross Domestic Product (GDP) per capita, Nominal Exchange Rate (NER), and the Nominal Interest Rate (NIR) from the Central Bank of Brazil. Our results indicate cross-correlated patterns that can be directly compared with the power-law spectra for multiple regimes. We have also identified cyclical patterns of high intensities that coincide with the Brazilian presidential elections. The MF-DCCHM uncovers non-explicit cyclic patterns, quantifies the relations of two non-stationary signals (noise effect removed), and has outstanding potential for mapping cross-regime patterns in multiple domains.

Complex systems in biology, climatology, medicine, and economy hold emergent properties such as non-linearity, adaptation, and self-organization. These emergent attributes can derive from large-scale relationships, connections, and interactive behavior despite not being apparent from their isolated components. It is possible to better comprehend complex systems by analyzing cross-correlations between time series. However, the accumulation of non-linear processes induces multiscale structures, therefore, a spectrum of power-law exponents (the fractal dimension) and distinct cyclical patterns. We propose the Multifractal Detrended Cross-Correlation Heatmaps (MF-DCCHM), a new method to map the relationships between fluctuations of signals on different time scales and regimes. Our dataset is composed of sales and inventory from the Brazilian automotive sector and macroeconomic descriptors, namely the Gross Domestic Product (GDP) per capita, Nominal Exchange Rate (NER), and the Nominal Interest Rate (NIR) from the Central Bank of Brazil. Our results indicate cross-correlated patterns that can be directly compared with the power-law spectra for multiple regimes. We have also identified cyclical patterns of high intensities that coincide with the Brazilian presidential elections. The MF-DCCHM uncovers non-explicit cyclic patterns, quantifies the relations of two non-stationary signals (noise effect removed), and has outstanding potential for mapping cross-regime patterns in multiple domains.