Symbolic analysis of bursting dynamical regimes of Rulkov neural networks

Neurons modeled by the Rulkov map display a variety of dynamic regimes that include tonic spikes and chaotic bursting. Here we study an ensemble of bursting neurons coupled with the Watts-Strogatz small-world topology. We characterize the sequences of bursts using the symbolic method of time-series analysis known as ordinal analysis, which detects nonlinear temporal correlations. We show that the probabilities of the different symbols distinguish different dynamical regimes, which depend on the coupling strength and the network topology. These regimes have different spatio-temporal properties that can be visualized with raster plots

Discriminating chaotic and stochastic time series using permutation entropy and artificial neural networks

Extracting relevant properties of empirical signals generated by nonlinear, stochastic, and high-dimensional systems is a challenge of complex systems research. Open questions are how to differentiate chaotic signals from stochastic ones, and how to quantify nonlinear and/or high-order temporal correlations. Here we propose a new technique to reliably address both problems. Our approach follows two steps: first, we train an artificial neural network (ANN) with flicker (colored) noise to predict the value of the parameter, $\alpha$, that determines the strength of the correlation of the noise. To predict $\alpha$ the ANN input features are a set of probabilities that are extracted from the time series by using symbolic ordinal analysis. Then, we input to the trained ANN the probabilities extracted from the time series of interest, and analyze the ANN output. We find that the $\alpha$ value returned by the ANN is informative of the temporal correlations present in the time series. To distinguish between stochastic and chaotic signals, we exploit the fact that the difference between the permutation entropy (PE) of a given time series and the PE of flicker noise with the same $\alpha$ parameter is small when the time series is stochastic, but it is large when the time series is chaotic. We validate our technique by analysing synthetic and empirical time series whose nature is well established. We also demonstrate the robustness of our approach with respect to the length of the time series and to the level of noise. We expect that our algorithm, which is freely available, will be very useful to the community

Small changes at single nodes can shift global network dynamics

Understanding the sensitivity of a system's behavior with respect to parameter changes is essential for many applications. This sensitivity may be desired - for instance in the brain, where a large repertoire of different dynamics, particularly different synchronization patterns, is crucial - or may be undesired - for instance in power grids, where disruptions to synchronization may lead to blackouts. In this work, we show that the dynamics of networks of phase oscillators can acquire a very large and complex sensitivity to changes made in either their units' parameters or in their connections - even modifications made to a parameter of a single unit can radically alter the global dynamics of the network in an unpredictable manner. As a consequence, each modification leads to a different path to phase synchronization manifested as large fluctuations along that path. This dynamical malleability occurs over a wide parameter region, around the network's two transitions to phase synchronization. One transition is induced by increasing the coupling strength between the units, and another is induced by increasing the prevalence of long-range connections. Specifically, we study Kuramoto phase oscillators connected under either Watts-Strogatz or distance-dependent topologies to analyze the statistical properties of the fluctuations along the paths to phase synchrony. We argue that this increase in the dynamical malleability is a general phenomenon, as suggested by both previous studies and the theory of phase transitions.Comment: 14 pages, 8 figure

Spatial permutation entropy distinguishes resting brain states

We use ordinal analysis and spatial permutation entropy to distinguish between eyes-open and eyes-closed resting brain states. To do so, we analyze EEG data recorded with 64 electrodes from 109 healthy subjects, under two one-minute baseline runs: One with eyes open, and one with eyes closed. We use spatial ordinal analysis to distinguish between these states, where the permutation entropy is evaluated considering the spatial distribution of electrodes for each time instant. We analyze both raw and post-processed data considering only the alpha-band frequency (8–12 Hz) which is known to be important for resting states in the brain. We conclude that spatial ordinal analysis captures information about correlations between time series in different electrodes. This allows the discrimination of eyes closed and eyes open resting states in both raw and filtered data. Filtering the data only amplifies the distinction between states. Importantly, our approach does not require EEG signal pre-processing, which is an advantage for real-time applications, such as brain-computer interfaces.B.R.R.B. and E.E.N.M. acknowledge support of São Paulo Research Foundation (FAPESP), Brazil, Proc. 2018/03211-6 and 2021/09839-0; and Financiadora de Estudos e Projetos (FINEP), Brazil. R.C.B. acknowledges support of Western Institute for Neuroscience Clinical Research Postdoctoral Fellowship and Western Academy for Advanced Research. K.L.R. acknowledges supported of German Academic Exchange Service (DAAD). C.M. acknowledges support of Ministerio de Ciencia, Innovación ������ Universidades (PID2021-123994NB-C21), Spain and Institució Catalana de Recerca i Estudis Avançats (ICREA), Spain.Peer ReviewedPostprint (published version

Wettbewerb und Regulierung

Wettbewerb und Regulierung werfen sowohl aus einer wirtschafts- als auch aus einer politikwissenschaftlichen Perspektive interessante Fragestellungen auf und haben daher in beiden Disziplinen umfangreiche Beachtung gefunden. Der vorliegende Beitrag gibt eine Übersicht über beide Herangehensweisen. Dabei wer-den zunächst die grundlegenden Unterschiede und Gemeinsamkeiten offengelegt (Abschnitt 2), bevor die disziplinären Schwerpunkte in der Analyse vorgestellt, und aus Sicht der jeweils anderen Disziplin kommentiert werden (Abschnitte 3 und 4). Wir kommen zu dem Ergebnis, dass beide Sichtweisen in erster Linie komplementär sind und sich gegenseitig befruchten können