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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 IX.Transfer entropy () values and significance as a function of the assumed delay  for two bidirectionally coupled, chaotic Lorenz systems. The simulated delays were  and . Observation noise with different amplitude was added to the simulated time series of the processes. The delays were recovered as (A)  and  for  (blue),  and (B)  for  (red) and  and  for  (green).
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pone-0055809-g016: Test case IX.Transfer entropy () values and significance as a function of the assumed delay for two bidirectionally coupled, chaotic Lorenz systems. The simulated delays were and . Observation noise with different amplitude was added to the simulated time series of the processes. The delays were recovered as (A) and for (blue), and (B) for (red) and and for (green).

Mentions: In test case (IX) we simulated two bidirectionally, quadratically coupled Lorenz systems with delays , , and added independent, Gaussian, white noise to the time series of the -coordinate (see equations 32, 33 for details) before the reconstruction of delays. Observation noise did degrade the precision of delay reconstruction to a certain degree: with 1%, 2% and 9% of the total signal variance contributed by noise, the estimated delays were , and (figure 16). Note that noise amplitude and delay reconstruction error do not seem to be systematically related, suggesting that the effects of particular realizations of finite data cause the reconstruction errors.


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 IX.Transfer entropy () values and significance as a function of the assumed delay  for two bidirectionally coupled, chaotic Lorenz systems. The simulated delays were  and . Observation noise with different amplitude was added to the simulated time series of the processes. The delays were recovered as (A)  and  for  (blue),  and (B)  for  (red) and  and  for  (green).
© Copyright Policy
Related In: Results  -  Collection

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

pone-0055809-g016: Test case IX.Transfer entropy () values and significance as a function of the assumed delay for two bidirectionally coupled, chaotic Lorenz systems. The simulated delays were and . Observation noise with different amplitude was added to the simulated time series of the processes. The delays were recovered as (A) and for (blue), and (B) for (red) and and for (green).
Mentions: In test case (IX) we simulated two bidirectionally, quadratically coupled Lorenz systems with delays , , and added independent, Gaussian, white noise to the time series of the -coordinate (see equations 32, 33 for details) before the reconstruction of delays. Observation noise did degrade the precision of delay reconstruction to a certain degree: with 1%, 2% and 9% of the total signal variance contributed by noise, the estimated delays were , and (figure 16). Note that noise amplitude and delay reconstruction error do not seem to be systematically related, suggesting that the effects of particular realizations of finite data cause the reconstruction errors.

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