Estimability and dependency analysis of model parameters based on delay coordinates

Schumann-Bischoff, Jan; Parlitz, Ulrich

doi:10.1103/physreve.94.032221

Cited by 12 publications

(18 citation statements)

References 45 publications

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“…EEG data, as well as data obtained from several other methods, is thus used to shed light into the binding connecting network structures678910 and the strengths of the neuron synapses in the brain. Modelling EEG signals is essential to understand the anatomy and histophysiology of the brain, and therefore provide support to medical imaging analysis and to the development of neuroscience11. However, consensus about what is the topology of the brain or its synaptic modus operandi is still an open problem.…”

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confidence: 99%

Weak connections form an infinite number of patterns in the brain

Ren

Bai

Baptista

et al. 2017

Sci Rep

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Recently, much attention has been paid to interpreting the mechanisms for memory formation in terms of brain connectivity and dynamics. Within the plethora of collective states a complex network can exhibit, we show that the phenomenon of Collective Almost Synchronisation (CAS), which describes a state with an infinite number of patterns emerging in complex networks for weak coupling strengths, deserves special attention. We show that a simulated neuron network with neurons weakly connected does produce CAS patterns, and additionally produces an output that optimally model experimental electroencephalograph (EEG) signals. This work provides strong evidence that the brain operates locally in a CAS regime, allowing it to have an unlimited number of dynamical patterns, a state that could explain the enormous memory capacity of the brain, and that would give support to the idea that local clusters of neurons are sufficiently decorrelated to independently process information locally.

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confidence: 99%

Weak connections form an infinite number of patterns in the brain

Ren

Bai

Baptista

et al. 2017

Sci Rep

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“…However, a weak linear correlation does not mean that there is no coupling relation between the variables. Previous studies (Sugihara et al, 2012;Emile-Geay and Tingley, 2016) have suggested that although the linear correlation of two variables is potentially absent, it might be nonlinearly coupled. For instance, the linear cross-correlations of sea air temperature series observed in different tropical areas are overall weak, but they can be strong locally and vary with time (Ludescher et al, 2014); such a time-varying correlation is an indicator of nonlinear correlation (Sugihara et al, 2012).…”

Section: Introductionmentioning

confidence: 98%

“…Previous studies (Sugihara et al, 2012;Emile-Geay and Tingley, 2016) have suggested that although the linear correlation of two variables is potentially absent, it might be nonlinearly coupled. For instance, the linear cross-correlations of sea air temperature series observed in different tropical areas are overall weak, but they can be strong locally and vary with time (Ludescher et al, 2014); such a time-varying correlation is an indicator of nonlinear correlation (Sugihara et al, 2012). These nonlinear correlations of the sea air temperature series have been found to be conductive to the better El Niño predictions (Ludescher et al, 2014;Conti et al, 2017).…”

Section: Introductionmentioning

confidence: 98%

“…One possible key factor is the coupling between different variables. Because different climate variables are coupled with one another in different ways (Donner and Large, 2008), the coupled variables will share their information content with one another through the information transfer (Takens, 1981;Schreiber, 2000;Sugihara et al, 2012). Furthermore, a coupling often results in the fact that the observational time series are statistically correlated (Brown, 1994).…”

Section: Introductionmentioning

confidence: 99%

“…The Pearson coefficient is often used to detect the correlation, but it can only detect the linear correlation. It is known that when the Pearson correlation coefficient is weak, most of the tasks based on traditional regression methods will fail at dealing with the climatic data, such as fitting, reconstruction, and prediction (Brown, 1994;Sugihara et al, 2012;Emile-Geay and Tingley, 2016). However, a weak linear correlation does not mean that there is no coupling relation between the variables.…”

Section: Introductionmentioning

confidence: 99%

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Reconstructing coupled time series in climate systems using three kinds of machine-learning methods

Huang

Yang

2020

Earth Syst. Dynam.

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Abstract. Despite the great success of machine learning, its application in climate dynamics has not been well developed. One concern might be how well the trained neural networks could learn a dynamical system and what will be the potential application of this kind of learning. In this paper, three machine-learning methods are used: reservoir computer (RC), backpropagation-based (BP) artificial neural network, and long short-term memory (LSTM) neural network. It shows that the coupling relations or dynamics among variables in linear or nonlinear systems can be inferred by RC and LSTM, which can be further applied to reconstruct one time series from the other. Specifically, we analyzed the climatic toy models to address two questions: (i) what factors significantly influence machine-learning reconstruction and (ii) how do we select suitable explanatory variables for machine-learning reconstruction. The results reveal that both linear and nonlinear coupling relations between variables do influence the reconstruction quality of machine learning. If there is a strong linear coupling between two variables, then the reconstruction can be bidirectional, and both of these two variables can be an explanatory variable for reconstructing the other. When the linear coupling among variables is absent but with the significant nonlinear coupling, the machine-learning reconstruction between two variables is direction dependent, and it may be only unidirectional. Then the convergent cross mapping (CCM) causality index is proposed to determine which variable can be taken as the reconstructed one and which as the explanatory variable. In a real-world example, the Pearson correlation between the average tropical surface air temperature (TSAT) and the average Northern Hemisphere SAT (NHSAT) is weak (0.08), but the CCM index of NHSAT cross mapped with TSAT is large (0.70). And this indicates that TSAT can be well reconstructed from NHSAT through machine learning. All results shown in this study could provide insights into machine-learning approaches for paleoclimate reconstruction, parameterization scheme, and prediction in related climate research.Highlights: i The coupling dynamics learned by machine learning can be used to reconstruct time series. ii Reconstruction quality is direction dependent and variable dependent for nonlinear systems. iii The CCM index is a potential indicator to choose reconstructed and explanatory variables. iv The tropical average SAT can be well reconstructed from the average Northern Hemisphere SAT.

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Nonlinear analysis of an indirectly controlled limit cycle walker

Tokuda

Asano

2018

Artif Life Robotics

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Estimability and dependency analysis of model parameters based on delay coordinates

Cited by 12 publications

References 45 publications

Weak connections form an infinite number of patterns in the brain

Weak connections form an infinite number of patterns in the brain

Reconstructing coupled time series in climate systems using three kinds of machine-learning methods

Nonlinear analysis of an indirectly controlled limit cycle walker

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