| Texto completo | |
| Autor(es): |
Vega-Oliveros, Didier A.
;
Mendez-Bermulez, J. A.
;
Rodrigues, Francisco A.
Número total de Autores: 3
|
| Tipo de documento: | Artigo Científico |
| Fonte: | PHYSICAL REVIEW E; v. 99, n. 4, p. 7-pg., 2019-04-10. |
| Resumo | |
In this paper we demonstrate numerically that random networks whose adjacency matrices A are represented by a diluted version of the power-law banded random matrix (PBRM) model have multifractal eigenfunctions. The PBRM model describes one-dimensional samples with random long-range bonds. The bond strengths of the model, which decay as a power-law, are tuned by the parameter mu as A(mm) proportional to vertical bar m - nVERBAR;(-mu ); while the sparsity is driven by the average network connectivity alpha: for alpha = 0 the vertices in the network are isolated and for alpha = 1 the network is fully connected and the PBRM model is recovered. Though it is known that the PBRM model has multifractal eigenfunctions at the critical value mu = mu(c) = 1, we clearly show [from the scaling of the relative fluctuation of the participation number I-2 as well as the scaling of the probability distribution functions P(ln I-2)] the existence of the critical value mu(c) (math) mu(c) (alpha) for alpha < 1. Moreover, we characterize the multifractality of the eigenfunctions of our random network model by the use of the corresponding multifractal dimensions D-q, that we compute from the finite network-size scaling of the typical eigenfunction participation numbers exp < ln I-q >. (AU) | |
| Processo FAPESP: | 13/07375-0 - CeMEAI - Centro de Ciências Matemáticas Aplicadas à Indústria |
| Beneficiário: | Francisco Louzada Neto |
| Modalidade de apoio: | Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs |
| Processo FAPESP: | 16/23698-1 - Processos Dinâmicos em Aprendizado de Máquina baseados em Redes Complexas |
| Beneficiário: | Didier Augusto Vega Oliveros |
| Modalidade de apoio: | Bolsas no Brasil - Pós-Doutorado |
| Processo FAPESP: | 13/26416-9 - Modelagem de processos dinâmicos em redes complexas |
| Beneficiário: | Francisco Aparecido Rodrigues |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |