Anomalous Lifshitz dimension in hierarchical networks of brain connectivity Esfandiary, Samaneh Safari, Ali Renner, Jakob Moretti, Paolo Muñoz Martínez, Miguel Ángel We acknowledge the Deutsche Forschungsgemeinschaft through Grants No. MO 3049/1-1, No. MO 3049/3-1, and No. GRK 2423 FRASCAL; the Spanish Ministry and Agencia Estatal de Investigación (AEI) through Grant No. FIS2017- 84256-P (European Regional Development Fund, ERDF); as well as FEDER/Junta de Andalucía-Consejería de Economía y Conocimiento/Projects (Refs. A-FQM-175-UGR18 and SOMM17/6105/UGR) for financial support. The spectral dimension is a generalization of the Euclidean dimension and quantifies the propensity of a network to transmit and diffuse information. We show that in hierarchical-modular network models of the brain, dynamics are anomalously slow and the spectral dimension is not defined. Inspired by Anderson localization in quantum systems, we relate the localization of neural activity—essential to embed brain functionality—to the network spectrum and to the existence of an anomalous “Lifshitz dimension.” In a broader context, our results help shed light on the relationship between structure and function in biological information-processing complex networks. 2021-03-03T08:51:35Z 2021-03-03T08:51:35Z 2020-11-30 journal article Samaneh Esfandiary, Ali Safari, Jakob Renner, Paolo Moretti, and Miguel A. Muñoz. Anomalous Lifshitz dimension in hierarchical networks of brain connectivity. Phys. Rev. Research 2, 043291 [https://doi.org/10.1103/PhysRevResearch.2.043291] http://hdl.handle.net/10481/66799 10.1103/PhysRevResearch.2.043291 eng http://creativecommons.org/licenses/by/3.0/es/ open access Atribución 3.0 España American Physical Society