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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

Interaction delay reconstruction in the turtle brain.(A) Electroretinogram (green), and LFP recordings (blue), light pulses are marked by yellow boxes. (B) Schematic depiction of stimulation and recording, including the investigated interactions and the identified delays.
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pone-0055809-g017: Interaction delay reconstruction in the turtle brain.(A) Electroretinogram (green), and LFP recordings (blue), light pulses are marked by yellow boxes. (B) Schematic depiction of stimulation and recording, including the investigated interactions and the identified delays.

Mentions: To demonstrate that interaction delays can be reconstructed from biological time series with sufficient precision, we analyzed recordings of the electroretinogram () and local field potentials from the tectum () of the turtle brain (Pseudemys scripta elegans, figure 17). These data were recorded during stimulation () with light flashes at time points determined by a random process and with a duration drawn from a uniform random distribution; this ensured stationarity of the time series. In this experiment, direct physical interactions existed from the light source to the retina and from the retina to the tectum (). In addition, there was an indirect interaction from the light source to the tectum, mediated by the retina. This opens the possibility to check the precision of the delay reconstruction despite the fact the we have no precise knowledge of the true biological interaction delays. The evaluation of reconstruction precision is possible because the interaction delays reconstructed from and from should sum up to the interaction delay reconstructed from if reconstruction is precise.


Measuring information-transfer delays.

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

Interaction delay reconstruction in the turtle brain.(A) Electroretinogram (green), and LFP recordings (blue), light pulses are marked by yellow boxes. (B) Schematic depiction of stimulation and recording, including the investigated interactions and the identified delays.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0055809-g017: Interaction delay reconstruction in the turtle brain.(A) Electroretinogram (green), and LFP recordings (blue), light pulses are marked by yellow boxes. (B) Schematic depiction of stimulation and recording, including the investigated interactions and the identified delays.
Mentions: To demonstrate that interaction delays can be reconstructed from biological time series with sufficient precision, we analyzed recordings of the electroretinogram () and local field potentials from the tectum () of the turtle brain (Pseudemys scripta elegans, figure 17). These data were recorded during stimulation () with light flashes at time points determined by a random process and with a duration drawn from a uniform random distribution; this ensured stationarity of the time series. In this experiment, direct physical interactions existed from the light source to the retina and from the retina to the tectum (). In addition, there was an indirect interaction from the light source to the tectum, mediated by the retina. This opens the possibility to check the precision of the delay reconstruction despite the fact the we have no precise knowledge of the true biological interaction delays. The evaluation of reconstruction precision is possible because the interaction delays reconstructed from and from should sum up to the interaction delay reconstructed from if reconstruction is precise.

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