@article{SchmidtZamoraLopezKurths2010,
  author    = {Schmidt, G. and Zamora-Lopez, Gorka and Kurths, J{\"u}rgen},
  title     = {Simulation of large scale cortical networks by individual neuron dynamics},
  issn      = {0218-1274},
  doi       = {10.1142/S0218127410026149},
  year      = {2010},
  abstract  = {Understanding the functional dynamics of the mammalian brain is one of the central aims of modern neuroscience. Mathematical modeling and computational simulations of neural networks can help in this quest. In recent publications, a multilevel model has been presented to simulate the resting-state dynamics of the cortico-cortical connectivity of the mammalian brain. In the present work we investigate how much of the dynamical behavior of the multilevel model can be reproduced by a strongly simplified model. We find that replacing each cortical area by a single Rulkov map recreates the patterns of dynamical correlation of the multilevel model, while the outcome of other models and setups mainly depends on the local network properties, e. g. the input degree of each vertex. In general, we find that a simple simulation whose dynamics depends on the global topology of the whole network is far from trivial. A systematic analysis of different dynamical models and coupling setups is required.},
  language  = {en}
}
@article{GomezGardenesZamoraLopezMorenoetal.2010,
  author    = {Gomez-Garde{\~n}es, Jes{\´u}s and Zamora-Lopez, Gorka and Moreno, Yamir and Arenas, Alexandre},
  title     = {From modular to centralized organization of synchronization in functional areas of the cat cerebral cortex},
  issn      = {1932-6203},
  doi       = {10.1371/journal.pone.0012313},
  year      = {2010},
  abstract  = {Recent studies have pointed out the importance of transient synchronization between widely distributed neural assemblies to understand conscious perception. These neural assemblies form intricate networks of neurons and synapses whose detailed map for mammals is still unknown and far from our experimental capabilities. Only in a few cases, for example the C. elegans, we know the complete mapping of the neuronal tissue or its mesoscopic level of description provided by cortical areas. Here we study the process of transient and global synchronization using a simple model of phase-coupled oscillators assigned to cortical areas in the cerebral cat cortex. Our results highlight the impact of the topological connectivity in the developing of synchronization, revealing a transition in the synchronization organization that goes from a modular decentralized coherence to a centralized synchronized regime controlled by a few cortical areas forming a Rich-Club connectivity pattern.},
  language  = {en}
}
@article{ArenasBorgeHolthoeferGomezetal.2010,
  author    = {Arenas, Alexandre and Borge-Holthoefer, Javier and Gomez, Sergio and Zamora-Lopez, Gorka},
  title     = {Optimal map of the modular structure of complex networks},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/12/5/053009},
  year      = {2010},
  abstract  = {The modular structure is pervasive in many complex networks of interactions observed in natural, social and technological sciences. Its study sheds light on the relation between the structure and the function of complex systems. Generally speaking, modules are islands of highly connected nodes separated by a relatively small number of links. Every module can have the contributions of links from any node in the network. The challenge is to disentangle these contributions to understand how the modular structure is built. The main problem is that the analysis of a certain partition into modules involves, in principle, as much data as the number of modules times the number of nodes. To confront this challenge, here we first define the contribution matrix, the mathematical object containing all the information about the partition of interest, and then we use truncated singular value decomposition to extract the best representation of this matrix in a plane. The analysis of this projection allows us to scrutinize the skeleton of the modular structure, revealing the structure of individual modules and their interrelations.},
  language  = {en}
}
@article{ZamoraLopezZhouKurths2009,
  author    = {Zamora-Lopez, Gorka and Zhou, Changsong and Kurths, J{\"u}rgen},
  title     = {Graph analysis of cortical networks reveals complex anatomical communication substrate},
  issn      = {1054-1500},
  doi       = {10.1063/1.3089559},
  year      = {2009},
  abstract  = {Sensory information entering the nervous system follows independent paths of processing such that specific features are individually detected. However, sensory perception, awareness, and cognition emerge from the combination of information. Here we have analyzed the corticocortical network of the cat, looking for the anatomical substrate which permits the simultaneous segregation and integration of information in the brain. We find that cortical communications are mainly governed by three topological factors of the underlying network: (i) a large density of connections, (ii) segregation of cortical areas into clusters, and (iii) the presence of highly connected hubs aiding the multisensory processing and integration. Statistical analysis of the shortest paths reveals that, while information is highly accessible to all cortical areas, the complexity of cortical information processing may arise from the rich and intricate alternative paths in which areas can influence each other.},
  language  = {en}
}