Quantifying sudden changes in dynamical systems using symbolic networks

Masoller, Cristina; Hong, Yanhua; Ayad, Sarah; Gustave, François; Barland, S.; Pons, Antonio J.; Gómez, Sergio; Arenas, Àlex

doi:10.1088/1367-2630/17/2/023068

Cited by 31 publications

(32 citation statements)

References 41 publications

(54 reference statements)

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“…It is worth noticing that other generalized algorithms for building ordinal networks from time series have been proposed and applied. These different numerical recipes include the use of non-overlapping partitions [10,27], partitions with time-lagged elements [25], and the inclusion of amplitude information about the time series elements [26]. Naturally, the constraints we have discussed here do not hold for these generalized algorithms.…”

Section: Methodsmentioning

confidence: 99%

Characterizing stochastic time series with ordinal networks

Pessa

Ribeiro

2019

Phys. Rev. E

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Approaches for mapping time series to networks have become essential tools for dealing with the increasing challenges of characterizing data from complex systems. Among the different algorithms, the recently proposed ordinal networks stand out due to its simplicity and computational efficiency. However, applications of ordinal networks have been mainly focused on time series arising from nonlinear dynamical systems, while basic properties of ordinal networks related to simple stochastic processes remain poorly understood. Here, we investigate several properties of ordinal networks emerging from random time series, noisy periodic signals, fractional Brownian motion, and earthquake magnitude series. For ordinal networks of random series, we present an approach for building the exact form of the adjacency matrix, which in turn is useful for detecting non-random behavior in time series and the existence of missing transitions among ordinal patterns. We find that the average value of a local entropy, estimated from transition probabilities among neighboring nodes of ordinal networks, is more robust against noise addition than the standard permutation entropy. We show that ordinal networks can be used for estimating the Hurst exponent of time series with accuracy comparable with state-of-the-art methods. Finally, we argue that ordinal networks can detect sudden changes in Earth seismic activity caused by large earthquakes. arXiv:1910.01406v1 [physics.data-an]

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Section: Methodsmentioning

confidence: 99%

Characterizing stochastic time series with ordinal networks

Pessa

Ribeiro

2019

Phys. Rev. E

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“…If the EEG signals are generated by fully random processes, all symbols are equally probable and the PE is maximum, P E = ln(D!). Additional diagnostic tools were proposed by Masoller et al 3 , which are based in the transition probabilities (TPs) between consecutive symbols defined from nonoverlapping data values. The transition probability from pattern π a to pattern π b is the relative number of times pattern π a is followed by pattern π b , in the sequence s(t):…”

Section: Methodsmentioning

confidence: 99%

Differentiating resting brain states using ordinal symbolic analysis

Quintero-Quiroz

Montesano²,

Pons

et al. 2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Symbolic methods of analysis are valuable tools for investigating complex time-dependent signals. In particular, the ordinal method defines sequences of symbols according to the ordering in which values appear in a time series. This method has been shown to yield useful information, even when applied to signals with large noise contamination. Here we use ordinal analysis to investigate the transition between eyes closed (EC) and eyes open (EO) resting states. We analyze two EEG datasets (with 71 and 109 healthy subjects) with different recording conditions (sampling rates and number of electrodes in the scalp). Using as diagnostic tools the permutation entropy, the entropy computed from symbolic transition probabilities, and an asymmetry coefficient (that measures the asymmetry of the likelihood of the transitions between symbols) we show that ordinal analysis applied to the raw data distinguishes the two brain states. In both datasets we find that the EO state is characterized by higher entropies and lower asymmetry coefficient, as compared to the EC state. Our results thus show that these diagnostic tools have potential for detecting and characterizing changes in time-evolving brain states.

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“…It allows to classify different types of behaviors [20,21], to detect dynamical changes [22][23][24], etc. (see [25,26] for many examples).…”

Section: Introductionmentioning

confidence: 99%

Emergence of spike correlations in periodically forced excitable systems

2016

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In sensory neurons the presence of noise can facilitate the detection of weak information-carrying signals, which are encoded and transmitted via correlated sequences of spikes. Here we investigate relative temporal order in spike sequences induced by a subthreshold periodic input, in the presence of white Gaussian noise. To simulate the spikes, we use the FitzHugh-Nagumo model, and to investigate the output sequence of inter-spike intervals (ISIs), we use the symbolic method of ordinal analysis. We find different types of relative temporal order, in the form of preferred ordinal patterns which depend on both, the strength of the noise and the period of the input signal. We also demonstrate a resonance-like behavior, as certain periods and noise levels enhance temporal ordering in the ISI sequence, maximizing the probability of the preferred patterns. Our findings could be relevant for understanding the mechanisms underlying temporal coding, by which single sensory neurons represent in spike sequences the information about weak periodic stimuli.

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Quantifying sudden changes in dynamical systems using symbolic networks

Cited by 31 publications

References 41 publications

Characterizing stochastic time series with ordinal networks

Characterizing stochastic time series with ordinal networks

Differentiating resting brain states using ordinal symbolic analysis

Emergence of spike correlations in periodically forced excitable systems

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