Diffusion of time-varying signals in cortical networks

The relationship between the structure and function of cortical networks is analyzed in terms of signal transmission between different cortical regions in the brains of cat and macaque, as modeled by the fundamental dynamics of diffusion. We investigated the relationship between modular network organization and diffused signal reception and verified that cortical areas in the same topological communities tend to receive signals with similar alterations. In addition, we modeled the diffusion dynamics on the network by a FIR filter whose coefficients correspond to the number of walks of different lengths between the source and destination nodes. Such an approach underlies the possibility to recover, at the destination node, the original signal provided the distribution of paths is known. We verified that the system functions obtained for regions belonging to different cortical communities present distinct roots, reinforcing the strict relationship between the structure and function in cortical networks.

[1]  H. Hotelling.  Analysis of a complex of statistical variables into principal components. , 1933 .

[2]  Stephen A. Dyer,et al.  Digital signal processing , 2018, 8th International Multitopic Conference, 2004. Proceedings of INMIC 2004..

[3]  L. D. Costa.  Diffusion of Time-Varying Signals in Complex Networks: A Structure-Dynamics Investigation Focusing the Distance to the Source of Activation , 2008, 0811.3783.

[4]  L. da F. Costa,et al.  Characterization of complex networks: A survey of measurements , 2005, cond-mat/0505185.

[5]  M. A. O'Neil,et al.  The connectional organization of the cortico-thalamic system of the cat. , 1999, Cerebral cortex.

[6]  Changsong Zhou,et al.  Hierarchical organization unveiled by functional connectivity in complex brain networks. , 2006, Physical review letters.

[7]  Marcus Kaiser,et al.  Clustered organization of cortical connectivity , 2007, Neuroinformatics.

[8]  Luciano da Fontoura Costa,et al.  Superedges: Connecting Structure and Dynamics in Complex Networks , 2008 .

[9]  O. Sporns,et al.  Organization, development and function of complex brain networks , 2004, Trends in Cognitive Sciences.

[10]  J. Kurths,et al.  Structure–function relationship in complex brain networks expressed by hierarchical synchronization , 2007 .

[11]  Cornelis J. Stam,et al.  Magnetoencephalographic evaluation of resting-state functional connectivity in Alzheimer's disease , 2006, NeuroImage.

[12]  L. da F. Costa,et al.  An analytical approach to neuronal connectivity , 2003, cond-mat/0306543.

[13]  C Koch,et al.  Complexity and the nervous system. , 1999, Science.

[14]  L. da F. Costa,et al.  A generalized approach to complex networks , 2006 .

[15]  Laura Astolfi,et al.  Cortical Network Dynamics during Foot Movements , 2008, Neuroinformatics.

[16]  Matthieu Latapy,et al.  Computing Communities in Large Networks Using Random Walks , 2004, J. Graph Algorithms Appl..

[17]  O. Sporns,et al.  Motifs in Brain Networks , 2004, PLoS biology.

[18]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[19]  Olaf Sporns,et al.  Networks analysis, complexity, and brain function , 2002 .

[20]  M P Young,et al.  Anatomical connectivity defines the organization of clusters of cortical areas in the macaque monkey and the cat. , 2000, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[21]  D. J. Felleman,et al.  Distributed hierarchical processing in the primate cerebral cortex. , 1991, Cerebral cortex.

[22]  L F Lago-Fernández,et al.  Fast response and temporal coherent oscillations in small-world networks. , 1999, Physical review letters.

[23]  Albert-László Barabási,et al.  Error and attack tolerance of complex networks , 2000, Nature.

[24]  O. Sporns.  Network Analysis , Complexity , and Brain Function , 2002 .

[25]  S. T. Buckland,et al.  An Introduction to the Bootstrap. , 1994 .

[26]  M. A. Yoder,et al.  Signal Processing First , 2003 .

[27]  Filipi Nascimento Silva,et al.  Hierarchical Characterization of Complex Networks , 2004, cond-mat/0412761.

[28]  Gilbert Strang,et al.  Introduction to applied mathematics , 1988 .

[29]  Luciano da Fontoura Costa,et al.  Correlating thalamocortical connectivity and activity , 2006 .

[30]  Luciano da Fontoura Costa,et al.  An Analytical Approach to Connectivity in Regular Neuronal Networks , 2003 .

[31]  C. Stam,et al.  Disturbed functional connectivity in brain tumour patients: Evaluation by graph analysis of synchronization matrices , 2006, Clinical Neurophysiology.

[32]  Jon H. Kaas,et al.  Why is Brain Size so Important:Design Problems and Solutions as Neocortex Gets Biggeror Smaller , 2000 .

[33]  O. Sporns,et al.  Identification and Classification of Hubs in Brain Networks , 2007, PloS one.

[34]  Luciano da Fontoura Costa,et al.  Shape Analysis and Classification: Theory and Practice , 2000 .

[35]  Keiji Tanaka,et al.  Inferotemporal cortex and object vision. , 1996, Annual review of neuroscience.

[36]  Marcus Kaiser,et al.  Criticality of spreading dynamics in hierarchical cluster networks without inhibition , 2007, 0802.2508.