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| Author(s): |
Suzana de Siqueira Santos
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | São Paulo. |
| Institution: | Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) |
| Defense date: | 2020-02-28 |
| Examining board members: |
André Fujita;
Joana Bisol Balardin;
Florencia Graciela Leonardi;
Fabricio Martins Lopes;
Francisco Aparecido Rodrigues
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| Advisor: | André Fujita |
| Abstract | |
Graphs are used to study the behavior of several systems, such as social and biological networks. In this context, a common problem is (i) selecting the random graph model and set of parameters that best fit the real world network and interpreting/predicting its behavior. Given a sequence of networks and observed values, we have additionally the problem (ii) of studying their interaction. For (i), Takahashi and colleagues proposed a method based on the spectral density (distribuition of the eigenvalues of the adjacency matrix) whose main advantage is its generality: it works for different random graph models. We proposed adaptations based on the l1 norm between spectral densities and between cumulative distributions of the eigenvalues, which led us to the derivation of theoretical results on the consistency of the parameter estimators. Finally, we study problem (ii) in the context of the Autism Spectrum Disorder (ASD), whose sub-groups Asperger and autism have little known neural bases. As there are evidences of alterations of the default mode network in ASD, we compared the relation between this network and the largest white matter structure of the brain (corpus callosum) between Asperger and autism. Our results suggest that this relation is greater in Asperger than in autism in the anterior region of the corpus callosum and that the largest eigenvalue can capture the relation with the estimated random graph parameter. (AU) | |
| FAPESP's process: | 15/21162-4 - Identification of variables associated with the graph structure and applications in neuroscience |
| Grantee: | Suzana de Siqueira Santos |
| Support Opportunities: | Scholarships in Brazil - Doctorate |