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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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Related in: MedlinePlus

Test case VIII.Transfer entropy () values and significance as a function of the assumed delay  for three unidirectionally coupled chaotic Lorenz systems. The First Lorenz couples with the second Lorenz with an interaction delay of  samples, the second Lorenz is unidirectionally coupled with the third Lorenz at a delay of  samples and the third Lorenz is unidirectionally coupled with the first Lorenz at an interaction delay of  samples. The reconstruction of the simulated delays were: (A) self feedback, , this value may be due to insufficient embedding, (B) , (C) , and (D).
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pone-0055809-g015: Test case VIII.Transfer entropy () values and significance as a function of the assumed delay for three unidirectionally coupled chaotic Lorenz systems. The First Lorenz couples with the second Lorenz with an interaction delay of samples, the second Lorenz is unidirectionally coupled with the third Lorenz at a delay of samples and the third Lorenz is unidirectionally coupled with the first Lorenz at an interaction delay of samples. The reconstruction of the simulated delays were: (A) self feedback, , this value may be due to insufficient embedding, (B) , (C) , and (D).

Mentions: In a network of three Lorenz systems coupled into a unidirectional ring, test case (VIII), our method identified the three simulated delays , , with reasonable precision as , , (figure 15). Analysis of self-feedback (as it is in principle present in a ring structure) for system resulted in no significant peak at the expected sum of all three simulated delays (90), indicating that the information originally transfered from system 1 into the ring is effectively wiped out by the chaotic dynamics of the next nodes in the ring, a phenomenon well known in from coupled chaotic laser systems [46].


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 VIII.Transfer entropy () values and significance as a function of the assumed delay  for three unidirectionally coupled chaotic Lorenz systems. The First Lorenz couples with the second Lorenz with an interaction delay of  samples, the second Lorenz is unidirectionally coupled with the third Lorenz at a delay of  samples and the third Lorenz is unidirectionally coupled with the first Lorenz at an interaction delay of  samples. The reconstruction of the simulated delays were: (A) self feedback, , this value may be due to insufficient embedding, (B) , (C) , and (D).
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC3585400&req=5

pone-0055809-g015: Test case VIII.Transfer entropy () values and significance as a function of the assumed delay for three unidirectionally coupled chaotic Lorenz systems. The First Lorenz couples with the second Lorenz with an interaction delay of samples, the second Lorenz is unidirectionally coupled with the third Lorenz at a delay of samples and the third Lorenz is unidirectionally coupled with the first Lorenz at an interaction delay of samples. The reconstruction of the simulated delays were: (A) self feedback, , this value may be due to insufficient embedding, (B) , (C) , and (D).
Mentions: In a network of three Lorenz systems coupled into a unidirectional ring, test case (VIII), our method identified the three simulated delays , , with reasonable precision as , , (figure 15). Analysis of self-feedback (as it is in principle present in a ring structure) for system resulted in no significant peak at the expected sum of all three simulated delays (90), indicating that the information originally transfered from system 1 into the ring is effectively wiped out by the chaotic dynamics of the next nodes in the ring, a phenomenon well known in from coupled chaotic laser systems [46].

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