The attractor structure of functional connectivity in coupled logistic maps.

Stylized models of dynamical processes on graphs allow us to explore the relationships between network architecture and dynamics, a topic of relevance in a range of disciplines. One strategy is to translate dynamical observations into pairwise relationships of nodes, often called functional connectivity (FC), and quantitatively compare them with network architecture or structural connectivity (SC). Here, we start from the observation that for coupled logistic maps, SC/FC relationships vary strongly with coupling strength. Using symbolic encoding, the mapping of the dynamics onto a cellular automaton, and the subsequent analysis of the resulting attractors, we show that this behavior is invariant under these transformations and can be understood from the attractors of the cellular automaton alone. Interestingly, noise enhances SC/FC correlations by creating a more uniform sampling of attractors. On a methodological level, we introduce cellular automata as a data analysis tool, rather than a simulation model of dynamics on graphs.

First activity and interactions in thalamus and cortex using raw single-trial EEG and MEG elicited by somatosensory stimulation.

Introduction: One of the primary motivations for studying the human brain is to comprehend how external sensory input is processed and ultimately perceived by the brain. A good understanding of these processes can promote the identification of biomarkers for the diagnosis of various neurological disorders; it can also provide ways of evaluating therapeutic techniques. In this work, we seek the minimal requirements for identifying key stages of activity in the brain elicited by median nerve stimulation. Methods: We have used a priori knowledge and applied a simple, linear, spatial filter on the electroencephalography and magnetoencephalography signals to identify the early responses in the thalamus and cortex evoked by short electrical stimulation of the median nerve at the wrist. The spatial filter is defined first from the average EEG and MEG signals and then refined using consistency selection rules across ST. The refined spatial filter is then applied to extract the timecourses of each ST in each targeted generator. These ST timecourses are studied through clustering to quantify the ST variability. The nature of ST connectivity between thalamic and cortical generators is then studied within each identified cluster using linear and non-linear algorithms with time delays to extract linked and directional activities. A novel combination of linear and non-linear methods provides in addition discrimination of influences as excitatory or inhibitory. Results: Our method identifies two key aspects of the evoked response. Firstly, the early onset of activity in the thalamus and the somatosensory cortex, known as the P14 and P20 in EEG and the second M20 for MEG. Secondly, good estimates are obtained for the early timecourse of activity from these two areas. The results confirm the existence of variability in ST brain activations and reveal distinct and novel patterns of connectivity in different clusters. Discussion: It has been demonstrated that we can extract new insights into stimulus processing without the use of computationally costly source reconstruction techniques which require assumptions and detailed modeling of the brain. Our methodology, thanks to its simplicity and minimal computational requirements, has the potential for real-time applications such as in neurofeedback systems and brain-computer interfaces.