Estimating the Entropy Rate of Spike Trains via Lempel-Ziv Complexity

Amigó, José M.; Szczepański, Janusz; Wajnryb, Eligiusz; Sanchez-Vives, Maria V.

doi:10.1162/089976604322860677

Cited by 148 publications

(154 citation statements)

References 15 publications

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“…Given that no specific visual stimuli were presented, we may assume that the spike trains are locally stationary, allowing us to estimate those parameters by means of 5-s long, sliding windows. The estimation of the necessary information and entropy rates was obtained by means of the normalized Lempel-Ziv complexity, a technique that the authors have studied in previous works; see, e.g., Szczepanski et al (2003), Amigó et al (2004). The encoding parameters and window length were chosen precisely on the grounds of our experience with this estimator.…”

Section: Discussionmentioning

confidence: 99%

“…This is an alternative to the analysis based on firing rate methods. It was shown that Lempel-Ziv complexity as defined in Lempel and Ziv (1976) can be used successfully as such an estimator (Amigó et al 2004).…”

Section: The Entropy Rate and The Lempel-ziv Estimatormentioning

confidence: 99%

“…This is important because periods of stationarity can be comparatively short. For more details, see Amigó et al (2004).…”

Section: The Entropy Rate and The Lempel-ziv Estimatormentioning

confidence: 99%

“…Thus, for the pair of spike trains (X, Y ) we obtain corresponding sequence of symbols (based on a four-letter alphabet) representing its joint distribution and, next, we calculate the normalized complexity with four letters formula (Amigó et al 2004), so the dimensionality of letters does not increase significantly.…”

Section: Relative Mutual Informationmentioning

confidence: 99%

“…The entropy rate of a locally stationary neural signal at time t is then estimated in the time window [t, t + T ]. We will use for this purpose the normalized Lempel-Ziv 76 complexity (Lempel and Ziv 1976), a technique we applied and tested in Amigó et al (2004). Precisely, the explicit analysis of locally stationary neural signals (along with the introduction of RMI) is perhaps the most important aspect of this article.…”

Section: Introductionmentioning

confidence: 99%

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Mutual information and redundancy in spontaneous communication between cortical neurons

et al. 2011

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An important question in neural information processing is how neurons cooperate to transmit information. To study this question, we resort to the concept of redundancy in the information transmitted by a group of neurons and, at the same time, we introduce a novel concept for measuring cooperation between pairs of neurons called relative mutual information (RMI). Specifically, we studied these two parameters for spike trains generated by neighboring neurons from the primary visual cortex in the awake, freely moving rat. The spike trains studied here were spontaneously generated in the cortical network, in the absence of visual stimulation. Under these conditions, our analysis revealed that while the value of RMI oscillated slightly around an average value, the redundancy exhibited a behavior character- ized by a higher variability. We conjecture that this combination of approximately constant RMI and greater variable redundancy makes information transmission more resistant to noise disturbances. Furthermore, the redundancy values suggest that neurons can cooperate in a flexible way during information transmission. This mostly occurs via a leading neuron with higher transmission rate or, less frequently, through the information rate of the whole group being higher than the sum of the individual information rates-in other words in a synergetic manner. The proposed method applies not only to the stationary, but also to locally stationary neural signals.

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Section: Discussionmentioning

confidence: 99%

Section: The Entropy Rate and The Lempel-ziv Estimatormentioning

confidence: 99%

“…This is important because periods of stationarity can be comparatively short. For more details, see Amigó et al (2004).…”

Section: The Entropy Rate and The Lempel-ziv Estimatormentioning

confidence: 99%

Section: Relative Mutual Informationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Mutual information and redundancy in spontaneous communication between cortical neurons

et al. 2011

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Non‐intrusive characterization of particle size changes in fluidized beds using recurrence plots

et al. 2016

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An on-line method is developed for monitoring of mean particle size in fluidized beds using pressure fluctuations (PFs) and acoustic emissions (AE) signal by recurrence plot (RP) and recurrence quantification analysis (RQA). PFs and AE signals of a lab-scale fluidized bed were measured simultaneously at various superficial gas velocities and mean particle sizes. Although the AE signals are often very complicated due to many different acoustic sources in the bed, applying RP analyses showed that small changes in mean particle size can be detected by visual comparison of AE-RP structures, while this cannot be distinguished by graphical RP analysis of PFs. Moreover, the hydrodynamics of the bed was inspected through RQA analysis of both signals. For this purpose, recurrence rate, determinism, laminarity, average length of diagonal and vertical lines were extracted from RPs showing the effect of an increase in the mean particle size.

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On using compressibility to detect when slime mould completed computation

Adamatzky

Jones

2015

Complexity

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Disclaimer UWE has obtained warranties from all depositors as to their title in the material deposited and as to their right to deposit such material. UWE makes no representation or warranties of commercial utility, title, or fitness for a particular purpose or any other warranty, express or implied in respect of any material deposited.UWE makes no representation that the use of the materials will not infringe any patent, copyright, trademark or other property or proprietary rights. UWE accepts no liability for any infringement of intellectual property rights in any material deposited but will remove such material from public view pending investigation in the event of an allegation of any such infringement. PLEASE SCROLL DOWN FOR TEXT.On using compressibility to detect when slime mould completed computation Abstract Slime mould Physarum polycephalum is a single cell visible by an unaided eye. The slime mould optimises its network of protoplasmic tubes in gradients of attractants and repellents. This behaviour is interpreted as computation. Several prototypes of the slime mould computers were designed to solve problems of computation geometry, graphs, transport networks and to implement universal computing circuits. Being a living substrate the slime mould does not halt its behaviour when a task is solved but often continues foraging the space thus masking the solution found. We propose to use temporal changes in compressibility of the slime mould patterns as indicators of the halting of the computation. Compressibility of a pattern characterises the pattern's morphological diversity, i.e. a number of different local configurations. At the beginning of computation the slime explores the space thus generating less compressible patterns. After gradients of attractants and repellents are detected the slime spans data sites with its protoplasmic network and retracts scouting branches, thus generating more compressible patterns. We analyse the feasibility of the approach on results of laboratory experiments and computer modelling.

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Estimating the Entropy Rate of Spike Trains via Lempel-Ziv Complexity

Cited by 148 publications

References 15 publications

Mutual information and redundancy in spontaneous communication between cortical neurons

Mutual information and redundancy in spontaneous communication between cortical neurons

Non‐intrusive characterization of particle size changes in fluidized beds using recurrence plots

On using compressibility to detect when slime mould completed computation

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