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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 (V).Transfer entropy () values and significance as a function of the assumed delay  for two bidirectionally coupled, chaotic Lorenz systems. The simulated delays were  and , and the coupling constants were . The delays were recovered as  and . For more parameters see table 2.
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pone-0055809-g008: Test case (V).Transfer entropy () values and significance as a function of the assumed delay for two bidirectionally coupled, chaotic Lorenz systems. The simulated delays were and , and the coupling constants were . The delays were recovered as and . For more parameters see table 2.

Mentions: For the analysis of two bidirectionally coupled Lorenz systems in test case (V), with and , transfer entropy values peaked at and samples for the interaction from process to , and to , respectively (Figure 8). These values differed only by one sample from to the true interaction delays used for simulation. Moreover, the relation between the transfer entropy values for the two coupling directions reversed with increasing delay parameter : for delay values up to 65, transfer entropy values were larger for the direction from process to , for values of larger than 65 the opposite was the case. This is an important finding as the difference of the transfer entropies in both directions, also called the net transfer entropy, is often used as an indicator of the effective or dominating interaction structure. However, in our example, this net information transfer changed sign with changing delay parameter . As an additional result, we show that the cross correlation function between the signals of the two systems was flat (Figure 9), as expected for a quadratic coupling.


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 (V).Transfer entropy () values and significance as a function of the assumed delay  for two bidirectionally coupled, chaotic Lorenz systems. The simulated delays were  and , and the coupling constants were . The delays were recovered as  and . For more parameters see table 2.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0055809-g008: Test case (V).Transfer entropy () values and significance as a function of the assumed delay for two bidirectionally coupled, chaotic Lorenz systems. The simulated delays were and , and the coupling constants were . The delays were recovered as and . For more parameters see table 2.
Mentions: For the analysis of two bidirectionally coupled Lorenz systems in test case (V), with and , transfer entropy values peaked at and samples for the interaction from process to , and to , respectively (Figure 8). These values differed only by one sample from to the true interaction delays used for simulation. Moreover, the relation between the transfer entropy values for the two coupling directions reversed with increasing delay parameter : for delay values up to 65, transfer entropy values were larger for the direction from process to , for values of larger than 65 the opposite was the case. This is an important finding as the difference of the transfer entropies in both directions, also called the net transfer entropy, is often used as an indicator of the effective or dominating interaction structure. However, in our example, this net information transfer changed sign with changing delay parameter . As an additional result, we show that the cross correlation function between the signals of the two systems was flat (Figure 9), as expected for a quadratic coupling.

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