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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 (VII) - self-feedback analysis.Transfer entropy () values between past and present of one of two Lorenz systems () and their significances as a function of the assumed delay  for a single chaotic Lorenz system subject to a feedback loop with delay , and an outgoing interaction  with delay . The recovered delay for the self feedback was , with a sidepeak at two times this value. For the interaction analysis  see figure 14. For more parameters see table 2.
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pone-0055809-g013: Test case (VII) - self-feedback analysis.Transfer entropy () values between past and present of one of two Lorenz systems () and their significances as a function of the assumed delay for a single chaotic Lorenz system subject to a feedback loop with delay , and an outgoing interaction with delay . The recovered delay for the self feedback was , with a sidepeak at two times this value. For the interaction analysis see figure 14. For more parameters see table 2.

Mentions: Second, we considered test case (VII) in which the feedback delay is longer than the interaction delay time (see Figures 13 and 14). In this case structure similar to test case (VI) is observed for the location of the peaks of . However, shows higher and more false positive peaks than in case (VI). This occurs since when , process can predict the transitions that will occur in already after a single delay loop, because even for the condition is fulfilled, – in contrast to a prediction of two delay loops ahead as in the previous case above. This situation is related to the so-called anticipative synchronization in which a slave system () can anticipate the dynamics of the master system when this is subject to a long feedback loop [44], [45].


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 (VII) - self-feedback analysis.Transfer entropy () values between past and present of one of two Lorenz systems () and their significances as a function of the assumed delay  for a single chaotic Lorenz system subject to a feedback loop with delay , and an outgoing interaction  with delay . The recovered delay for the self feedback was , with a sidepeak at two times this value. For the interaction analysis  see figure 14. For more parameters see table 2.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0055809-g013: Test case (VII) - self-feedback analysis.Transfer entropy () values between past and present of one of two Lorenz systems () and their significances as a function of the assumed delay for a single chaotic Lorenz system subject to a feedback loop with delay , and an outgoing interaction with delay . The recovered delay for the self feedback was , with a sidepeak at two times this value. For the interaction analysis see figure 14. For more parameters see table 2.
Mentions: Second, we considered test case (VII) in which the feedback delay is longer than the interaction delay time (see Figures 13 and 14). In this case structure similar to test case (VI) is observed for the location of the peaks of . However, shows higher and more false positive peaks than in case (VI). This occurs since when , process can predict the transitions that will occur in already after a single delay loop, because even for the condition is fulfilled, – in contrast to a prediction of two delay loops ahead as in the previous case above. This situation is related to the so-called anticipative synchronization in which a slave system () can anticipate the dynamics of the master system when this is subject to a long feedback loop [44], [45].

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