MACIEL CALEBE VIDAL
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Artigo Científico Correlation between graphs with an application to brain network analysis(2017) Fujita, André; Takahashi, Daniel Yasumasa; Balardin, Joana Bisol; MACIEL CALEBE VIDAL; Sato, João RicardoThe global functional brain network (graph) is more suitable for characterizing brain states than local analysis of the connectivity of brain regions. Therefore, graph-theoretic approaches are natural methods to use for studying the brain. However, conventional graph theoretical analyses are limited due to the lack of formal statistical methods of estimation and inference. For example, the concept of correlation between two vectors of graphs has not yet been defined. Thus, the introduction of a notion of correlation between graphs becomes necessary to better understand how brain sub-networks interact. To develop a framework to infer correlation between graphs, one may assume that they are generated by models and that the parameters of the models are the random variables. Then, it is possible to define that two graphs are independent when the random variables representing their parameters are independent. In the real world, however, the model is rarely known, and consequently, the parameters cannot be estimated. By analyzing the graph spectrum, it is shown that the spectral radius is highly associated with the parameters of the graph model. Based on this, a framework for correlation inference between graphs is constructed and the approach illustrated on functional magnetic resonance imaging data on 814 subjects comprising 529 controls and 285 individuals diagnosed with autism spectrum disorder (ASD). Results show that correlations between the default-mode and control, default-mode and somatomotor, and default-mode and visual sub-networks are higher in individuals with ASD than in the controls.Artigo Científico Granger Causality among Graphs and Application to Functional Brain Connectivity in Autism Spectrum Disorder(2021) Ribeiro, Adèle Helena; MACIEL CALEBE VIDAL; Sato, João Ricardo; Fujita, AndréGraphs/networks have become a powerful analytical approach for data modeling. Besides, with the advances in sensor technology, dynamic time-evolving data have become more common. In this context, one point of interest is a better understanding of the information flow within and between networks. Thus, we aim to infer Granger causality (G-causality) between networks’ time series. In this case, the straightforward application of the well-established vector autoregressive model is not feasible. Consequently, we require a theoretical framework for modeling time-varying graphs. One possibility would be to consider a mathematical graph model with time-varying parameters (assumed to be random variables) that generates the network. Suppose we identify G-causality between the graph models’ parameters. In that case, we could use it to define a G-causality between graphs. Here, we show that even if the model is unknown, the spectral radius is a reasonable estimate of some random graph model parameters. We illustrate our proposal’s application to study the relationship between brain hemispheres of controls and children diagnosed with Autism Spectrum Disorder (ASD). We show that the G-causality intensity from the brain’s right to the left hemisphere is different between ASD and controls.