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Measuring information-transfer delays.

Wibral M, Pampu N, Priesemann V, Siebenhühner F, Seiwert H, Lindner M, Lizier JT, Vicente R - PLoS ONE (2013)

Bottom Line: In complex networks such as gene networks, traffic systems or brain circuits it is important to understand how long it takes for the different parts of the network to effectively influence one another.We also show the ability of the extended transfer entropy to detect the presence of multiple delays, as well as feedback loops.While evaluated on neuroscience data, we expect the estimator to be useful in other fields dealing with network dynamics.

View Article: PubMed Central - PubMed

Affiliation: MEG Unit, Brain Imaging Center, Goethe University, Frankfurt, Germany. wibral@em.uni-frankfurt.de

ABSTRACT
In complex networks such as gene networks, traffic systems or brain circuits it is important to understand how long it takes for the different parts of the network to effectively influence one another. In the brain, for example, axonal delays between brain areas can amount to several tens of milliseconds, adding an intrinsic component to any timing-based processing of information. Inferring neural interaction delays is thus needed to interpret the information transfer revealed by any analysis of directed interactions across brain structures. However, a robust estimation of interaction delays from neural activity faces several challenges if modeling assumptions on interaction mechanisms are wrong or cannot be made. Here, we propose a robust estimator for neuronal interaction delays rooted in an information-theoretic framework, which allows a model-free exploration of interactions. In particular, we extend transfer entropy to account for delayed source-target interactions, while crucially retaining the conditioning on the embedded target state at the immediately previous time step. We prove that this particular extension is indeed guaranteed to identify interaction delays between two coupled systems and is the only relevant option in keeping with Wiener's principle of causality. We demonstrate the performance of our approach in detecting interaction delays on finite data by numerical simulations of stochastic and deterministic processes, as well as on local field potential recordings. We also show the ability of the extended transfer entropy to detect the presence of multiple delays, as well as feedback loops. While evaluated on neuroscience data, we expect the estimator to be useful in other fields dealing with network dynamics.

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Test case (VI).Transfer entropy () values and significance as a function of the assumed delay  for a unidirectionally coupled chaotic Lorenz systems. The first Lorenz is subject to a feedback loop () and unidirectionally couples to a second Lorenz with a interaction delay of  samples. Recovered delays were  (see figure 11), and . Sidepeaks were observed for  close to . Spurious interactions were observed in the reversed direction at , as it is expect for a system with self feedback [45]. Considering the positive test for self-feeback (figure 11) and the recovery of the self-feedback delay, the true system connectivity can be derived by combining the analysis of self-feedback and interaction delays.
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pone-0055809-g012: Test case (VI).Transfer entropy () values and significance as a function of the assumed delay for a unidirectionally coupled chaotic Lorenz systems. The first Lorenz is subject to a feedback loop () and unidirectionally couples to a second Lorenz with a interaction delay of samples. Recovered delays were (see figure 11), and . Sidepeaks were observed for close to . Spurious interactions were observed in the reversed direction at , as it is expect for a system with self feedback [45]. Considering the positive test for self-feeback (figure 11) and the recovery of the self-feedback delay, the true system connectivity can be derived by combining the analysis of self-feedback and interaction delays.

Mentions: Transfer entropy () values between past and present of one of two Lorenz systems () and significances as a function of the assumed delay . The analyzed chaotic Lorenz system was subject to a feedback loop with delay , and an outgoing interaction with delay , but no incoming interaction. The recovered delay for the self feedback was , with a sidepeak at around two times this value. For the interaction analysis see figure 12. For more parameters see table 2.


Measuring information-transfer delays.

Wibral M, Pampu N, Priesemann V, Siebenhühner F, Seiwert H, Lindner M, Lizier JT, Vicente R - PLoS ONE (2013)

Test case (VI).Transfer entropy () values and significance as a function of the assumed delay  for a unidirectionally coupled chaotic Lorenz systems. The first Lorenz is subject to a feedback loop () and unidirectionally couples to a second Lorenz with a interaction delay of  samples. Recovered delays were  (see figure 11), and . Sidepeaks were observed for  close to . Spurious interactions were observed in the reversed direction at , as it is expect for a system with self feedback [45]. Considering the positive test for self-feeback (figure 11) and the recovery of the self-feedback delay, the true system connectivity can be derived by combining the analysis of self-feedback and interaction delays.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3585400&req=5

pone-0055809-g012: Test case (VI).Transfer entropy () values and significance as a function of the assumed delay for a unidirectionally coupled chaotic Lorenz systems. The first Lorenz is subject to a feedback loop () and unidirectionally couples to a second Lorenz with a interaction delay of samples. Recovered delays were (see figure 11), and . Sidepeaks were observed for close to . Spurious interactions were observed in the reversed direction at , as it is expect for a system with self feedback [45]. Considering the positive test for self-feeback (figure 11) and the recovery of the self-feedback delay, the true system connectivity can be derived by combining the analysis of self-feedback and interaction delays.
Mentions: Transfer entropy () values between past and present of one of two Lorenz systems () and significances as a function of the assumed delay . The analyzed chaotic Lorenz system was subject to a feedback loop with delay , and an outgoing interaction with delay , but no incoming interaction. The recovered delay for the self feedback was , with a sidepeak at around two times this value. For the interaction analysis see figure 12. For more parameters see table 2.

Bottom Line: In complex networks such as gene networks, traffic systems or brain circuits it is important to understand how long it takes for the different parts of the network to effectively influence one another.We also show the ability of the extended transfer entropy to detect the presence of multiple delays, as well as feedback loops.While evaluated on neuroscience data, we expect the estimator to be useful in other fields dealing with network dynamics.

View Article: PubMed Central - PubMed

Affiliation: MEG Unit, Brain Imaging Center, Goethe University, Frankfurt, Germany. wibral@em.uni-frankfurt.de

ABSTRACT
In complex networks such as gene networks, traffic systems or brain circuits it is important to understand how long it takes for the different parts of the network to effectively influence one another. In the brain, for example, axonal delays between brain areas can amount to several tens of milliseconds, adding an intrinsic component to any timing-based processing of information. Inferring neural interaction delays is thus needed to interpret the information transfer revealed by any analysis of directed interactions across brain structures. However, a robust estimation of interaction delays from neural activity faces several challenges if modeling assumptions on interaction mechanisms are wrong or cannot be made. Here, we propose a robust estimator for neuronal interaction delays rooted in an information-theoretic framework, which allows a model-free exploration of interactions. In particular, we extend transfer entropy to account for delayed source-target interactions, while crucially retaining the conditioning on the embedded target state at the immediately previous time step. We prove that this particular extension is indeed guaranteed to identify interaction delays between two coupled systems and is the only relevant option in keeping with Wiener's principle of causality. We demonstrate the performance of our approach in detecting interaction delays on finite data by numerical simulations of stochastic and deterministic processes, as well as on local field potential recordings. We also show the ability of the extended transfer entropy to detect the presence of multiple delays, as well as feedback loops. While evaluated on neuroscience data, we expect the estimator to be useful in other fields dealing with network dynamics.

Show MeSH
Related in: MedlinePlus