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We investigate interaction networks that we derive from multivariate time series with methods frequently employed in diverse scientific fields such as biology, quantitative finance, physics, earth and climate sciences, and the neurosciences. Mimicking experimental situations, we generate time series with finite length and varying frequency content but from independent stochastic processes. Using the correlation coefficient and the maximum cross-correlation, we estimate interdependencies between these time series. With clustering coefficient and average shortest path length, we observe unweighted interaction networks, derived via thresholding the values of interdependence, to possess non-trivial topologies as compared to Erdös-Rényi networks, which would indicate small-world characteristics. These topologies reflect the mostly unavoidable finiteness of the data, which limits the reliability of typically used estimators of signal interdependence. We propose random networks that are tailored to the way interaction networks are derived from empirical data. Through an exemplary investigation of multichannel electroencephalographic recordings of epileptic seizures – known for their complex spatial and temporal dynamics – we show that such random networks help to distinguish network properties of interdependence structures related to seizure dynamics from those spuriously induced by the applied methods of analysis.
Rationale: Previous studies [Topolnik et al., Cereb Cortex 2003; 13: 883; Schindler et al., Brain 2007; 130: 65] indicate that the termination of focal onset seizures may be causally related to an increase of global neuronal correlation during the second half of the seizures. This increase was observed to occur earlier in complex partial seizures than in secondarily generalized seizures. We here address the question whether such an increase of neuronal correlation prior to seizure end is indeed a global phenomenon, involving both hemispheres or whether there are side-specific differences. Methods: We analyzed 20 focal onset seizures (10 complex partial, 10 secondarily generalized seizures) recorded in 13 patients who underwent presurgical evaluation of focal epilepsies of different origin. EEG was recorded intracranially from bilaterally implanted subdural strip and intrahippocampal depth electrodes. Utilizing a moving window approach, we investigated the evolution of the maximum cross correlation for all channel combinations during seizures. For each moving window the mean value of the maximum cross correlation (MCC) between all electrode contacts was computed separately for each hemisphere. After normalization of seizure durations, MCC values of the ipsi- and contralateral hemisphere for all seizures were determined. Results: We observed that the MCC of the contralateral hemisphere in complex partial seizures increased during the first half of the seizure, whereas, for the same time interval, the MCC of the ipsilateral hemisphere even declined below the level of the pre-seizure period. In contrast, no significant differences between both hemispheres could be observed for secondarily generalized seizures where both hemispheres showed a simultaneous increase of MCC during the second half of the seizures. The level of MCC for the contralateral hemisphere was higher for complex partial seizures than for secondarily generalized seizures during the first half of the seizure. Conclusions: Our findings indicate that there are indeed lateralized differences in the evolution of global neuronal correlation during complex partial and secondarily generalized seizures. The observed contralateral increase of neuronal correlation during complex partial seizures might indicate an emerging self-organizing mechanism for preventing the spread of seizure activity.
We consider recent reports on small-world topologies of interaction networks derived from the dynamics of spatially extended systems that are investigated in diverse scientific fields such as neurosciences, geophysics, or meteorology. With numerical simulations that mimic typical experimental situations, we have identified an important constraint when characterizing such networks: indications of a small-world topology can be expected solely due to the spatial sampling of the system along with the commonly used time series analysis based approaches to network characterization.
The stimulation and dominance of potentially harmful phytoplankton taxa at a given locale and time are determined by local environmental conditions as well as by transport to or from neighboring regions. The present study investigated the occurrence of common harmful algal bloom (HAB) taxa within the Southern California Bight, using cross-correlation functions to determine potential dependencies between HAB taxa and environmental factors, and potential links to algal transport via local hydrography and currents. A simulation study, in which Lagrangian particles were released, was used to assess travel times due to advection by prevailing ocean currents in the bight. Our results indicate that transport of some taxa may be an important mechanism for the expansion of their distributions into other regions, which was supported by mean travel times derived from our simulation study and other literature on ocean currents in the Southern California Bight. In other cases, however, phytoplankton dynamics were rather linked to local environmental conditions, including coastal upwelling events. Overall, our study shows that complex current patterns in the Southern California Bight may contribute significantly to the formation and expansion of HABs in addition to local environmental factors determining the spatiotemporal dynamics of phytoplankton blooms.