A graph-theoretical approach in brain functional networks. Possible implications in EEG studies

Abstract Background Recently, it was realized that the functional connectivity networks estimated from actual brain-imaging technologies (MEG, fMRI and EEG) can be analyzed by means of the graph theory, that is a mathematical representation of a network, which is essentially reduced to nodes and connections between them. Methods We used high-resolution EEG technology to enhance the poor spatial information of the EEG activity on the scalp and it gives a measure of the electrical activity on the cortical surface. Afterwards, we used the Directed Transfer Function (DTF) that is a multivariate spectral measure for the estimation of the directional influences between any given pair of channels in a multivariate dataset. Finally, a graph theoretical approach was used to model the brain networks as graphs. These methods were used to analyze the structure of cortical connectivity during the attempt to move a paralyzed limb in a group (N=5) of spinal cord injured patients and during the movement execution in a group (N=5) of healthy subjects. Results Analysis performed on the cortical networks estimated from the group of normal and SCI patients revealed that both groups present few nodes with a high out-degree value (i.e. outgoing links). This property is valid in the networks estimated for all the frequency bands investigated. In particular, cingulate motor areas (CMAs) ROIs act as ‘‘hubs’’ for the outflow of information in both groups, SCI and healthy. Results also suggest that spinal cord injuries affect the functional architecture of the cortical network sub-serving the volition of motor acts mainly in its local feature property. In particular, a higher local efficiency El can be observed in the SCI patients for three frequency bands, theta (3-6 Hz), alpha (7-12 Hz) and beta (13-29 Hz). By taking into account all the possible pathways between different ROI couples, we were able to separate clearly the network properties of the SCI group from the CTRL group. In particular, we report a sort of compensatory mechanism in the SCI patients for the Theta (3-6 Hz) frequency band, indicating a higher level of “activation” Ω within the cortical network during the motor task. The activation index is directly related to diffusion, a type of dynamics that underlies several biological systems including possible spreading of neuronal activation across several cortical regions. Conclusions The present study aims at demonstrating the possible applications of graph theoretical approaches in the analyses of brain functional connectivity from EEG signals. In particular, the methodological aspects of the i) cortical activity from scalp EEG signals, ii) functional connectivity estimations iii) graph theoretical indexes are emphasized in the present paper to show their impact in a real application.

The local power of the gradient test

The asymptotic expansion of the distribution of the gradient test statistic is derived for a composite hypothesis under a sequence of Pitman alternative hypotheses converging to the null hypothesis at rate n(-1/2), n being the sample size. Comparisons of the local powers of the gradient, likelihood ratio, Wald and score tests reveal no uniform superiority property. The power performance of all four criteria in one-parameter exponential family is examined.

Local order and electronic structure of Pb1-xLaxZr0.40Ti0.60O3 materials and its relation with ferroelectric properties

The knowledge of electronic and local structures is a fundamental step towards understanding the properties of ferroelectric ceramics. X-ray absorption near-edge structure (XANES) of Pb1-xLaxZr0.40Ti0.60O3 ferroelectric samples was measured in order to know how the local order and electronic structure are related to their ferroelectric property, which was tailored by the substitution of lead by lanthanum atoms. The analysis of XANES spectra collected at Ti K- and L-edges XANES showed that the substitution of Pb by La leads to a decrement of local distortion around Ti atoms on the TiO6 octahedron. The analysis of O K-edge XANES spectra showed that the hybridization between O 2p and Pb 6sp states is related to the displacement of Ti atoms in the TiO6 octahedra. Based on these results, it is possible to determine that the degree of ferroelectricity in these samples and the manifestation of relaxor behavior are directly related to the weakening of O 2p and Pb 6sp hybridization. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4720472]