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Temporal correlations in neuronal avalanche occurrence.

Lombardi F, Herrmann HJ, Plenz D, de Arcangelis L - Sci Rep (2016)

Bottom Line: Moreover we evidence that sizes of consecutive avalanches are correlated.In particular, we show that an avalanche tends to be larger or smaller than the following one for short or long time separation, respectively.Our analysis represents the first attempt to provide a quantitative estimate of correlations between activity and quiescence in the framework of neuronal avalanches and will help to enlighten the mechanisms underlying spontaneous activity.

View Article: PubMed Central - PubMed

Affiliation: Institute of Computational Physics for Engineering Materials, ETH, Zurich, Switzerland.

ABSTRACT
Ongoing cortical activity consists of sequences of synchronized bursts, named neuronal avalanches, whose size and duration are power law distributed. These features have been observed in a variety of systems and conditions, at all spatial scales, supporting scale invariance, universality and therefore criticality. However, the mechanisms leading to burst triggering, as well as the relationship between bursts and quiescence, are still unclear. The analysis of temporal correlations constitutes a major step towards a deeper understanding of burst dynamics. Here, we investigate the relation between avalanche sizes and quiet times, as well as between sizes of consecutive avalanches recorded in cortex slice cultures. We show that quiet times depend on the size of preceding avalanches and, at the same time, influence the size of the following one. Moreover we evidence that sizes of consecutive avalanches are correlated. In particular, we show that an avalanche tends to be larger or smaller than the following one for short or long time separation, respectively. Our analysis represents the first attempt to provide a quantitative estimate of correlations between activity and quiescence in the framework of neuronal avalanches and will help to enlighten the mechanisms underlying spontaneous activity.

No MeSH data available.


Related in: MedlinePlus

Conditional probability in experimental and reshuffled time series. (black circles) is the distribution of  for s0 = 300 μV and t0 = 300 ms, evaluated on 105 realizations of the reshuffled avalanche series. The distribution  is well fitted by a Gaussian (red curve) with mean value Q(si < s0, Δti < t0) = 0.5536 (black vertical line) and standard deviation σ(si < s0, Δti < t0) = 0.0094. The evaluation of P(si < s0/Δti < t0) in the real avalanche series for the same s0 and t0 provides the value 0.8269 (blue vertical line). It follows , indicating that significant correlations exist between the avalanche size and the following quiet time.
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f2: Conditional probability in experimental and reshuffled time series. (black circles) is the distribution of for s0 = 300 μV and t0 = 300 ms, evaluated on 105 realizations of the reshuffled avalanche series. The distribution is well fitted by a Gaussian (red curve) with mean value Q(si < s0, Δti < t0) = 0.5536 (black vertical line) and standard deviation σ(si < s0, Δti < t0) = 0.0094. The evaluation of P(si < s0/Δti < t0) in the real avalanche series for the same s0 and t0 provides the value 0.8269 (blue vertical line). It follows , indicating that significant correlations exist between the avalanche size and the following quiet time.

Mentions: We calculate the conditional probability (1) both for the avalanche time series and for several independent realizations of time series obtained by reshuffling avalanche sizes while keeping fixed their starting and ending times. We denote with a value of si randomly chosen in the entire time series and with the conditional probability (1) calculated in the reshuffled time series. We evaluate the distribution obtained from 105 realizations of reshuffled time series, which, as expected, is Gaussian because is uncorrelated to Δti by construction. We denote its mean value as and its standard deviation as (Fig. 2).


Temporal correlations in neuronal avalanche occurrence.

Lombardi F, Herrmann HJ, Plenz D, de Arcangelis L - Sci Rep (2016)

Conditional probability in experimental and reshuffled time series. (black circles) is the distribution of  for s0 = 300 μV and t0 = 300 ms, evaluated on 105 realizations of the reshuffled avalanche series. The distribution  is well fitted by a Gaussian (red curve) with mean value Q(si < s0, Δti < t0) = 0.5536 (black vertical line) and standard deviation σ(si < s0, Δti < t0) = 0.0094. The evaluation of P(si < s0/Δti < t0) in the real avalanche series for the same s0 and t0 provides the value 0.8269 (blue vertical line). It follows , indicating that significant correlations exist between the avalanche size and the following quiet time.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4837393&req=5

f2: Conditional probability in experimental and reshuffled time series. (black circles) is the distribution of for s0 = 300 μV and t0 = 300 ms, evaluated on 105 realizations of the reshuffled avalanche series. The distribution is well fitted by a Gaussian (red curve) with mean value Q(si < s0, Δti < t0) = 0.5536 (black vertical line) and standard deviation σ(si < s0, Δti < t0) = 0.0094. The evaluation of P(si < s0/Δti < t0) in the real avalanche series for the same s0 and t0 provides the value 0.8269 (blue vertical line). It follows , indicating that significant correlations exist between the avalanche size and the following quiet time.
Mentions: We calculate the conditional probability (1) both for the avalanche time series and for several independent realizations of time series obtained by reshuffling avalanche sizes while keeping fixed their starting and ending times. We denote with a value of si randomly chosen in the entire time series and with the conditional probability (1) calculated in the reshuffled time series. We evaluate the distribution obtained from 105 realizations of reshuffled time series, which, as expected, is Gaussian because is uncorrelated to Δti by construction. We denote its mean value as and its standard deviation as (Fig. 2).

Bottom Line: Moreover we evidence that sizes of consecutive avalanches are correlated.In particular, we show that an avalanche tends to be larger or smaller than the following one for short or long time separation, respectively.Our analysis represents the first attempt to provide a quantitative estimate of correlations between activity and quiescence in the framework of neuronal avalanches and will help to enlighten the mechanisms underlying spontaneous activity.

View Article: PubMed Central - PubMed

Affiliation: Institute of Computational Physics for Engineering Materials, ETH, Zurich, Switzerland.

ABSTRACT
Ongoing cortical activity consists of sequences of synchronized bursts, named neuronal avalanches, whose size and duration are power law distributed. These features have been observed in a variety of systems and conditions, at all spatial scales, supporting scale invariance, universality and therefore criticality. However, the mechanisms leading to burst triggering, as well as the relationship between bursts and quiescence, are still unclear. The analysis of temporal correlations constitutes a major step towards a deeper understanding of burst dynamics. Here, we investigate the relation between avalanche sizes and quiet times, as well as between sizes of consecutive avalanches recorded in cortex slice cultures. We show that quiet times depend on the size of preceding avalanches and, at the same time, influence the size of the following one. Moreover we evidence that sizes of consecutive avalanches are correlated. In particular, we show that an avalanche tends to be larger or smaller than the following one for short or long time separation, respectively. Our analysis represents the first attempt to provide a quantitative estimate of correlations between activity and quiescence in the framework of neuronal avalanches and will help to enlighten the mechanisms underlying spontaneous activity.

No MeSH data available.


Related in: MedlinePlus