Complex networks in brain electrical activity

We analyze the complex networks associated with brain electrical activity. Multichannel EEG measurements are first processed to obtain 3D voxel activations using the tomographic algorithm LORETA. Then, the correlation of the current intensity activation between voxel pairs is computed to produce a voxel cross-correlation coefficient matrix. Using several correlation thresholds, the cross-correlation matrix is then transformed into a network connectivity matrix and analyzed. To study a specific example, we selected data from an earlier experiment focusing on the MMN brain wave. The resulting analysis highlights significant differences between the spatial activations associated with Standard and Deviant tones, with interesting physiological implications. When compared to random data networks, physiological networks are more connected, with longer links and shorter path lengths. Furthermore, as compared to the Deviant case, Standard data networks are more connected, with longer links and shorter path lengths--i.e., with a stronger ``small worlds'' character. The comparison between both networks shows that areas known to be activated in the MMN wave are connected. In particular, the analysis supports the idea that supra-temporal and inferior frontal data work together in the processing of the differences between sounds by highlighting an increased connectivity in the response to a novel sound.Comment: 22 pages, 5 figures. Starlab preprint. This version is an attempt to include better figures (no content change

Fluctuations of Complex Networks: Electrical Properties of Single Protein Nanodevices

We present for the first time a complex network approach to the study of the electrical properties of single protein devices. In particular, we consider an electronic nanobiosensor based on a G-protein coupled receptor. By adopting a coarse grain description, the protein is modeled as a complex network of elementary impedances. The positions of the alpha-carbon atoms of each amino acid are taken as the nodes of the network. The amino acids are assumed to interact electrically among them. Consequently, a link is drawn between any pair of nodes neighboring in space within a given distance and an elementary impedance is associated with each link. The value of this impedance can be related to the physical and chemical properties of the amino acid pair and to their relative distance. Accordingly, the conformational changes of the receptor induced by the capture of the ligand, are translated into a variation of its electrical properties. Stochastic fluctuations in the value of the elementary impedances of the network, which mimic different physical effects, have also been considered. Preliminary results concerning the impedance spectrum of the network and its fluctuations are presented and discussed for different values of the model parameters.Comment: 16 Pages and 10 Figures published in SPIE Proceedings of the II International Symposium on Fluctuation and Noise, Maspalomas,Gran Canaria,Spain, 25-28 May 200

Adjacent Graph Based Vulnerability Assessment for Electrical Networks Considering Fault Adjacent Relationships Among Branches

Security issues related to vulnerability assessment in electrical networks are necessary for operators to identify the critical branches. At present, using complex network theory to assess the structural vulnerability of the electrical network is a popular method. However, the complex network theory cannot be comprehensively applicable to the operational vulnerability assessment of the electrical network because the network operation is closely dependent on the physical rules not only on the topological structure. To overcome the problem, an adjacent graph (AG) considering the topological, physical, and operational features of the electrical network is constructed to replace the original network. Through the AG, a branch importance index that considers both the importance of a branch and the fault adjacent relationships among branches is constructed to evaluate the electrical network vulnerability. The IEEE 118-bus system and the French grid are employed to validate the effectiveness of the proposed method.National Natural Science Foundation of China under Grant U1734202National Key Research and Development Plan of China under Grant 2017YFB1200802-12National Natural Science Foundation of China under Grant 51877181National Natural Science Foundation of China under Grant 61703345Chinese Academy of Sciences, under Grant 2018-2019-0

Apparatus for statistical time-series analysis of electrical signals

An apparatus for performing statistical time-series analysis of complex electrical signal waveforms, permitting prompt and accurate determination of statistical characteristics of the signal is presented

Lipschitz stability for the electrical impedance tomography problem: the complex case

In this paper we investigate the boundary value problem {div(\gamma\nabla u)=0 in \Omega, u=f on \partial\Omega where $\gamma$ is a complex valued $L^\infty$ coefficient, satisfying a strong ellipticity condition. In Electrical Impedance Tomography, $\gamma$ represents the admittance of a conducting body. An interesting issue is the one of determining $\gamma$ uniquely and in a stable way from the knowledge of the Dirichlet-to-Neumann map $\Lambda_\gamma$. Under the above general assumptions this problem is an open issue. In this paper we prove that, if we assume a priori that $\gamma$ is piecewise constant with a bounded known number of unknown values, then Lipschitz continuity of $\gamma$ from $\Lambda_\gamma$ holds

Complex Impedance as a Diagnostic Tool for Characterizing Thermal Detectors

The complex ac impedance of a bolometer or microcalorimeter detector is easily measured and can be used to determine thermal time constants, thermal resistances, heat capacities, and sensitivities. Accurately extracting this information requires an understanding of the electrical and thermal properties of both the detector and the measurement system. We show that this is a practical method for measuring parameters in detectors with moderately complex thermal systems.Comment: 7 pages, 5 figures, RevTeX, Review of Scientific Instruments, in pres

Activity-dependent neuronal model on complex networks

Neuronal avalanches are a novel mode of activity in neuronal networks, experimentally found in vitro and in vivo, and exhibit a robust critical behaviour: These avalanches are characterized by a power law distribution for the size and duration, features found in other problems in the context of the physics of complex systems. We present a recent model inspired in self-organized criticality, which consists of an electrical network with threshold firing, refractory period and activity-dependent synaptic plasticity. The model reproduces the critical behaviour of the distribution of avalanche sizes and durations measured experimentally. Moreover, the power spectra of the electrical signal reproduce very robustly the power law behaviour found in human electroencephalogram (EEG) spectra. We implement this model on a variety of complex networks, i.e. regular, small-world and scale-free and verify the robustness of the critical behaviour.Comment: 9 pages, 8 figure

Electrical Treeing in Silicone Rubber

Electrical treeing has been widely studied in a range of polymeric materials. In these investigations, the morphology and PD patterns associated with the growth of electrical trees in a model transparent silicone rubber were investigated using a new system recently developed at Southampton. With increasing voltage the trees became more complex in appearance but nevertheless grow more rapidly. As the tree evolves the PD pattern becomes more intense which may provide a method of monitoring the extent of treeing in opaque samples. Raman studies indicate that treeing and breakdown channels are hollow, carbonaceous entities, a finding consistent with other studies

Comparing the Topological and Electrical Structure of the North American Electric Power Infrastructure

The topological (graph) structure of complex networks often provides valuable information about the performance and vulnerability of the network. However, there are multiple ways to represent a given network as a graph. Electric power transmission and distribution networks have a topological structure that is straightforward to represent and analyze as a graph. However, simple graph models neglect the comprehensive connections between components that result from Ohm's and Kirchhoff's laws. This paper describes the structure of the three North American electric power interconnections, from the perspective of both topological and electrical connectivity. We compare the simple topology of these networks with that of random (Erdos and Renyi, 1959), preferential-attachment (Barabasi and Albert, 1999) and small-world (Watts and Strogatz, 1998) networks of equivalent sizes and find that power grids differ substantially from these abstract models in degree distribution, clustering, diameter and assortativity, and thus conclude that these topological forms may be misleading as models of power systems. To study the electrical connectivity of power systems, we propose a new method for representing electrical structure using electrical distances rather than geographic connections. Comparisons of these two representations of the North American power networks reveal notable differences between the electrical and topological structure of electric power networks