Statistical complexity is maximized close to criticality in cortical dynamics.

Complex systems are typically characterized as an intermediate situation between a complete regular structure and a random system. Brain signals can be studied as a striking example of such systems: cortical states can range from highly synchronous and ordered neuronal activity (with higher spiking variability) to desynchronized and disordered regimes (with lower spiking variability). It has been recently shown, by testing independent signatures of criticality, that a phase transition occurs in a cortical state of intermediate spiking variability. Here we use a symbolic information approach to show that, despite the monotonical increase of the Shannon entropy between ordered and disordered regimes, we can determine an intermediate state of maximum complexity based on the Jensen disequilibrium measure. More specifically, we show that statistical complexity is maximized close to criticality for cortical spiking data of urethane-anesthetized rats, as well as for a network model of excitable elements that presents a critical point of a nonequilibrium phase transition.

Dynamic functional connectivity in temporal lobe epilepsy: a graph theoretical and machine learning approach.

PURPOSE: Functional magnetic resonance imaging (fMRI) in resting state can be used to evaluate the functional organization of the human brain in the absence of any task or stimulus. The functional connectivity (FC) has non-stationary nature and consented to be varying over time. By considering the dynamic characteristics of the FC and using graph theoretical analysis and a machine learning approach, we aim to identify the laterality in cases of temporal lobe epilepsy (TLE). METHODS: Six global graph measures are extracted from static and dynamic functional connectivity matrices using fMRI data of 35 unilateral TLE subjects. Alterations in the time trend of the graph measures are quantified. The random forest (RF) method is used for the determination of feature importance and selection of dynamic graph features including mean, variance, skewness, kurtosis, and Shannon entropy. The selected features are used in the support vector machine (SVM) classifier to identify the left and right epileptogenic sides in patients with TLE. RESULTS: Our results for the performance of SVM demonstrate that the utility of dynamic features improves the classification outcome in terms of accuracy (88.5% for dynamic features compared with 82% for static features). Selecting the best dynamic features also elevates the accuracy to 91.5%. CONCLUSION: Accounting for the non-stationary characteristics of functional connectivity, dynamic connectivity analysis of graph measures along with machine learning approach can identify the temporal trend of some specific network features. These network features may be used as potential imaging markers in determining the epileptogenic hemisphere in patients with TLE.

Signatures of brain criticality unveiled by maximum entropy analysis across cortical states.

It has recently been reported that statistical signatures of brain criticality, obtained from distributions of neuronal avalanches, can depend on the cortical state. We revisit these claims with a completely different and independent approach, employing a maximum entropy model to test whether signatures of criticality appear in urethane-anesthetized rats. To account for the spontaneous variation of cortical states, we parse the time series and perform the maximum entropy analysis as a function of the variability of the population spiking activity. To compare data sets with different numbers of neurons, we define a normalized distance to criticality that takes into account the peak and width of the specific heat curve. We found a universal collapse of the normalized distance to criticality dependence on the cortical state, on an animal by animal basis. This indicates a universal dynamics and a critical point at an intermediate value of spiking variability.

Ultraviolet solar flare signatures in the framework of complex network.

Studying natural phenomena via the complex network approach makes it possible to quantify the time-evolving structures with too many elements and achieve a deeper understanding of interactions among the components of a system. In this sense, solar flare as a complex system with the chaotic behavior could be better characterized by the network parameters. Here, we employed an unsupervised network-based method to recognize the position and occurrence time of the solar flares by using the ultraviolet emission (1600 Å) recorded by the Atmospheric Imaging Assembly on board Solar Dynamics Observatory. Three different regions, the flaring active regions, the non-flaring active regions, and the quiet-Sun regions, were considered to study the variations of the network parameters in the presence and absence of flaring phases in various datasets over time intervals of several hours. The whole parts of the selected datasets were partitioned into sub-windows to construct networks based on computing the Pearson correlation between time series of the region of interest and intensities. Analyzing the network parameters such as the clustering coefficient, degree centrality, characteristic length, and PageRank verified that flare triggering has an influence on the network parameters around the flare occurrence time and close to the location of flaring. It was found that the values of the clustering coefficient and characteristic length approach those obtained for the corresponding random network in the flaring phase. These findings could be used for detecting the occurrence times and locations of the region at ultraviolet images.

Insights into the assembly rules of a continent-wide multilayer network.

How are ecological systems assembled? Identifying common structural patterns within complex networks of interacting species has been a major challenge in ecology, but researchers have focused primarily on single interaction types aggregating in space or time. Here, we shed light on the assembly rules of a multilayer network formed by frugivory and nectarivory interactions between bats and plants in the Neotropics. By harnessing a conceptual framework known as the integrative hypothesis of specialization, our results suggest that phylogenetic constraints separate species into different layers and shape the network's modules. Then, the network shifts to a nested structure within its modules where interactions are mainly structured by geographic co-occurrence. Finally, organismal traits related to consuming fruits or nectar determine which bat species are central or peripheral to the network. Our results provide insights into how different processes contribute to the assemblage of ecological systems at different levels of organization, resulting in a compound network topology.

Evolution of Graph Theory in Dynamic Functional Connectivity for Lateralization of Temporal Lobe Epilepsy.

Resting-state functional magnetic resonance imaging (rsfMRI) has described the functional architecture of the human brain in the absence of any task or stimulus. Since the functional connectivity (FC), has non-stationary nature, it is evidenced to be varying over time. Using dynamic functional connectivity, six graph theoretical characteristics were measured and compared between left and right temporal lobe epilepsy (TLE). We also obtain a trend for each characteristic in the time course of experiments. The results demonstrated that the static connectivity analysis failed to fully separate the left and right TLE patients for some characteristics, whereby the dynamic analysis has been shown capable of identifying the laterality. Furthermore, the results suggest that the temporal trend of some graph theoretical characteristics can be exploited as a novel marker for TLE laterality.

Centrality in earthquake multiplex networks.

Seismic time series has been mapped as a complex network, where a geographical region is divided into square cells that represent the nodes and connections are defined according to the sequence of earthquakes. In this paper, we map a seismic time series to a temporal network, described by a multiplex network, and characterize the evolution of the network structure in terms of the eigenvector centrality measure. We generalize previous works that considered the single layer representation of earthquake networks. Our results suggest that the multiplex representation captures better earthquake activity than methods based on single layer networks. We also verify that the regions with highest seismological activities in Iran and California can be identified from the network centrality analysis. The temporal modeling of seismic data provided here may open new possibilities for a better comprehension of the physics of earthquakes.

The role of community structure on the nature of explosive synchronization.

In this paper, we analyze explosive synchronization in networks with a community structure. The results of our study indicate that the mesoscopic structure of the networks could affect the synchronization of coupled oscillators. With the variation of three parameters, the degree probability distribution exponent, the community size probability distribution exponent, and the mixing parameter, we could have a fast or slow phase transition. Besides, in some cases, we could have communities which are synchronized inside but not with other communities and vice versa. We also show that there is a limit in these mesoscopic structures which suppresses the transition from the second-order phase transition and results in explosive synchronization. This could be considered as a tuning parameter changing the transition of the system from the second order to the first order.