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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

Overview over the structure of simulated test cases II-IX.Note that not all combination of links and parameters are always investigated. For details refer to table 2.
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pone-0055809-g004: Overview over the structure of simulated test cases II-IX.Note that not all combination of links and parameters are always investigated. For details refer to table 2.

Mentions: Figure 4 presents the general structure of test cases (II-VII,IX). All these cases comprise two systems labeled as , which are either both autoregressive order 10 processes (AR(10), equation 29), or both Lorenz systems (Lorenz, equation 32). For the Lorenz systems, the second coordinate ( - see equation 32) was used as the observable producing the time series used for analysis. The systems may interact in the direction , with either a single delay , or a set of delays , with coupling strengths or , respectively. In the reverse direction we only consider the case of single interactions with parameters , and . Additionally, in some of the cases delayed self feedback is present from process to process , with delay , and strength . All simulated interactions, including self-feedback, were non-linear (quadratic) functions. One additional case (VIII) investigates delay reconstruction from a unidirectionally coupled ring structure of three Lorenz systems; the last case (IX) simulates the effects of observation noise on delay reconstruction. Details of the test cases are presented in table 2. For each test cases 50 data segments (trials) of 3000 sampling points each were simulated, resulting in a total of 150.000 data points. A full description of the generating equations for the system dynamics and the simulation details can be found in the subsection on the test cases in the methods section. In the following, we present results for these eight test cases (II-IX), with test case (V) serving as an example for the inability of the ‘old’ estimator [9], [12], [13], [29] to recover the correct interaction delays.


Measuring information-transfer delays.

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

Overview over the structure of simulated test cases II-IX.Note that not all combination of links and parameters are always investigated. For details refer to table 2.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0055809-g004: Overview over the structure of simulated test cases II-IX.Note that not all combination of links and parameters are always investigated. For details refer to table 2.
Mentions: Figure 4 presents the general structure of test cases (II-VII,IX). All these cases comprise two systems labeled as , which are either both autoregressive order 10 processes (AR(10), equation 29), or both Lorenz systems (Lorenz, equation 32). For the Lorenz systems, the second coordinate ( - see equation 32) was used as the observable producing the time series used for analysis. The systems may interact in the direction , with either a single delay , or a set of delays , with coupling strengths or , respectively. In the reverse direction we only consider the case of single interactions with parameters , and . Additionally, in some of the cases delayed self feedback is present from process to process , with delay , and strength . All simulated interactions, including self-feedback, were non-linear (quadratic) functions. One additional case (VIII) investigates delay reconstruction from a unidirectionally coupled ring structure of three Lorenz systems; the last case (IX) simulates the effects of observation noise on delay reconstruction. Details of the test cases are presented in table 2. For each test cases 50 data segments (trials) of 3000 sampling points each were simulated, resulting in a total of 150.000 data points. A full description of the generating equations for the system dynamics and the simulation details can be found in the subsection on the test cases in the methods section. In the following, we present results for these eight test cases (II-IX), with test case (V) serving as an example for the inability of the ‘old’ estimator [9], [12], [13], [29] to recover the correct interaction delays.

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