Causal entropies—A measure for determining changes in the temporal organization of neural systems

Waddell, Jack N.; Dzakpasu, Rhonda; Booth, Victoria; Riley, Brett T.; Reasor, Jonathan; Poe, Gina R.; Żochowski, Michał

doi:10.1016/j.jneumeth.2006.12.008

Cited by 18 publications

(11 citation statements)

References 37 publications

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“…The idea that information in spike times relates to an underlying directed relationship has been observed, e.g., in [58] and regarding "causal entropy" in [59,60], which indeed computed entropies of (cross) inter-spike intervals. However to our knowledge, this is the first formulation that computes transfer entropy based on lossless representation of entire spike trains (and is thus a dynamic quantity which captures state-updates rather than static correlations of single spike-time relationships).…”

Section: Application To Spike Trainsmentioning

confidence: 98%

Transfer entropy in continuous time, with applications to jump and neural spiking processes

2017

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Transfer entropy has been used to quantify the directed flow of information between source and target variables in many complex systems. While transfer entropy was originally formulated in discrete time, in this paper we provide a framework for considering transfer entropy in continuous time systems, based on Radon-Nikodym derivatives between measures of complete path realizations. To describe the information dynamics of individual path realizations, we introduce the pathwise transfer entropy, the expectation of which is the transfer entropy accumulated over a finite time interval. We demonstrate that this formalism permits an instantaneous transfer entropy rate. These properties are analogous to the behavior of physical quantities defined along paths such as work and heat. We use this approach to produce an explicit form for the transfer entropy for pure jump processes, and highlight the simplified form in the specific case of point processes (frequently used in neuroscience to model neural spike trains). Finally, we present two synthetic spiking neuron model examples to exhibit the pertinent features of our formalism, namely, that the information flow for point processes consists of discontinuous jump contributions (at spikes in the target) interrupting a continuously varying contribution (relating to waiting times between target spikes). Numerical schemes based on our formalism promise significant benefits over existing strategies based on discrete time formalisms.

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Section: Application To Spike Trainsmentioning

confidence: 98%

Transfer entropy in continuous time, with applications to jump and neural spiking processes

2017

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“…More recent developments aim at estimating Granger causality directly from Fourier and wavelet transforms (Dhamala et al, 2008), rely on partial (Frenzel and Pompe, 2007) or conditional mutual information Vejmelka and Paluš, 2008), or make use of entropy estimates (Waddell et al, 2007;Liang, 2008). In order to improve the estimation of transfer entropy (Schreiber, 2000), Lungarella et al (2007) proposed a wavelet-based extension of this measure, and introduced symbolic transfer entropy as a robust and computationally fast method to quantify the dominating direction of information flow between time series.…”

Section: Bivariate Time Series Analysis Techniquesmentioning

confidence: 99%

Synchronization phenomena in human epileptic brain networks

Lehnertz

Bialonski

Horstmann

et al. 2009

Journal of Neuroscience Methods

228

147

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“…Finally, other measure proposed to estimate coupling between time series is the causal entropy (CauEn) [25]. This index is an asymmetric, time-adaptive, event-based measure of the regularity of the phase-or time-lag with which point i fires after point j.…”

Section: Irregularity Quantificationmentioning

confidence: 99%

“…It is calculated from two components: a non-parametric time-adaptive estimate of the probability density of spike time lag between two points i and j such that i follows j (and, independently, the distribution of j following i), and a cost function estimate of the spread and stability of the distribution. Although a variety of alternatives exists to compute this metric, CauEn can be easily estimated by choosing an event-normalized histogram as the time-adaptive density estimator and the ShEn as the cost function [25].…”

Section: Irregularity Quantificationmentioning

confidence: 99%

The Contribution of Nonlinear Methods in the Understanding of Atrial Fibrillation

Alcaraz¹,

Rieta²

2013

Atrial Fibrillation - Mechanisms and Treatment

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Additionally, the f wave analysis from surface ECG recordings is complicated by the simultaneous presence of VA, which is of much higher amplitude. Thereby, the dissociation of atrial and ventricular components is mandatory [12]. Nowadays, several methods to extract the AA signal from surface ECG recordings exist. The most powerful techniques are those that exploit the spatial diversity of the multilead ECG, such as the method that solves the blind source separation problem [3] or the spatiotemporal QRST cancellation strategy [13]. However, the performance of these techniques is seriously reduced when recordings are obtained from Holter systems for paroxysmal AF analysis. The reason is that, generally, Holter systems use no more than two or three leads, which are not enough to exploit the ECG spatial information. For single-lead applications, the most widely used alternative to extract the AA is the averaged beat subtraction (ABS). This method relies on the assumption that the average beat can represent, approximately, each individual beat [12]. Recently, a variety of extensions for this method have been proposed [12,14]. Intraatrial EGMNowadays, a variety of intraatrial recording modalities exists, such as bipolar and unipolar recordings from endocardial and epicardial electrodes, optical mapping and noncontact Atrial Fibrillation -Mechanisms and Treatment 182 mapping [15]. Although recordings from each one of these modalities have their own characteristics, unipolar recordings are generally characterized by a substantial far-field contamination, such as VA, whereas bipolar recordings contains local atrial activations of the place in which the electrodes are located. Nonetheless, these recordings are also affected by ventricular interference, especially in recording sites closer to the ventricles, even if its effect is less evident than on unipolar EGMs and surface ECG recordings. Thereby, for the VA cancellation both from unipolar and bipolar recordings, an averaged ventricular interference complex, as in ABS, is usually computed and subtracted from each atrial signal [16,17]. Only remark that the ventricular activations are habitually detected from a surface ECG recording simultaneously acquired for more accuracy.On the other hand, given that atrial dynamics can be analyzed both from simple EGMs and local atrial period (LAP) series, i.e., the sequence of temporal distances between two consecutive local atrial activations, the appropriate identification of these points is a important task in this context. For this purpose, EGMs are habitually high-pass filtering (40-250 Hz) to remove baseline shifts and high-frequency noise [18]. The filtered signal is then rectified, introducing low-frequency components related to the amplitude of the high-frequency oscillations of the original signal. The modulus of the filtered signal is further low-pass filtered (cut-off at 20 Hz) to extract a waveform proportional to the amplitude of the components of occurring at 40-250 Hz. The atrial activations are then detected by thr...

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Causal entropies—A measure for determining changes in the temporal organization of neural systems

Cited by 18 publications

References 37 publications

Transfer entropy in continuous time, with applications to jump and neural spiking processes

Transfer entropy in continuous time, with applications to jump and neural spiking processes

Synchronization phenomena in human epileptic brain networks

The Contribution of Nonlinear Methods in the Understanding of Atrial Fibrillation

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