更改

where <math>P(S)</math> is the probability of observing an avalanche of size <math>S\ ,</math> <math>\alpha</math> is the exponent that gives the slope of the power law in a log-log graph, and <math>k</math> is a proportionality constant. For experiments with [[slice culture]]s, the size distribution of avalanches of [[local field potential]]s has an exponent <math>\alpha\approx 1.5\ ,</math> but in recordings of spikes from a different array the exponent is <math>\alpha\approx2.1\ .</math> The reasons behind this difference in exponents are still being explored. It is important to note that a power law distribution is not what would be expected if activity at each electrode were driven independently. An ensemble of uncoupled, Poisson-like processes would lead to an exponential distribution of event sizes. Further, while power laws have been reported for many years in neuroscience in the temporal correlations of single time-series data (e.g., the power spectrum from [[Electroencephalogram|EEG]] (Linkenkaer-Hansen et al, 2001; Worrell et al, 2002), [[Fano factor|Fano]] or [[Allan factor]]s in [[Spike Statistics|spike count statistics]] (Teich et al, 1997), [[neurotransmitter]] secretion times (Lowen et al, 1997), [[ion channel]] fluctuations (Toib et al, 1998), interburst intervals in neuronal cultures (Segev et al, 2002)), they had not been observed from interactions seen in multielectrode data. Thus neuronal avalanches emerge from collective processes in a distributed network.

where <math>P(S)</math> is the probability of observing an avalanche of size <math>S\ ,</math> <math>\alpha</math> is the exponent that gives the slope of the power law in a log-log graph, and <math>k</math> is a proportionality constant. For experiments with [[slice culture]]s, the size distribution of avalanches of [[local field potential]]s has an exponent <math>\alpha\approx 1.5\ ,</math> but in recordings of spikes from a different array the exponent is <math>\alpha\approx2.1\ .</math> The reasons behind this difference in exponents are still being explored. It is important to note that a power law distribution is not what would be expected if activity at each electrode were driven independently. An ensemble of uncoupled, Poisson-like processes would lead to an exponential distribution of event sizes. Further, while power laws have been reported for many years in neuroscience in the temporal correlations of single time-series data (e.g., the power spectrum from [[Electroencephalogram|EEG]] (Linkenkaer-Hansen et al, 2001; Worrell et al, 2002), [[Fano factor|Fano]] or [[Allan factor]]s in [[Spike Statistics|spike count statistics]] (Teich et al, 1997), [[neurotransmitter]] secretion times (Lowen et al, 1997), [[ion channel]] fluctuations (Toib et al, 1998), interburst intervals in neuronal cultures (Segev et al, 2002)), they had not been observed from interactions seen in multielectrode data. Thus neuronal avalanches emerge from collective processes in a distributed network.

===Repeating avalanche patterns重复的雪崩模式===

===重复的雪崩模式===

[[Image:Figure5.jpg|thumb|200px|left|Families of repeating avalanches from an acute slice. Each family (1-4) shows a group of three similar avalanches.  Similarity within each group was higher than expected by chance when compared to 50 sets of shuffled data. Repeating avalanches also occur in cortical [[slice culture]]s, where there are on average 30 ± 14 (mean ± s.d.) distinct families of reproducible avalanches, each containing about 23 avalanches (Beggs and Plenz, 2004). Repeating avalanches are stable for 10 hrs and have a temporal precision of 4 ms, suggesting that they could serve as a substrate for storing information in [[neural networks]].]]  

[[Image:Figure5.jpg|thumb|200px|left|Families of repeating avalanches from an acute slice. Each family (1-4) shows a group of three similar avalanches.  Similarity within each group was higher than expected by chance when compared to 50 sets of shuffled data. Repeating avalanches also occur in cortical [[slice culture]]s, where there are on average 30 ± 14 (mean ± s.d.) distinct families of reproducible avalanches, each containing about 23 avalanches (Beggs and Plenz, 2004). Repeating avalanches are stable for 10 hrs and have a temporal precision of 4 ms, suggesting that they could serve as a substrate for storing information in [[neural networks]].]]  

While avalanches in [[critical sandpile models]] are stochastic in the patterns they form, avalanches of [[local field potentials]] occur in spatio-temporal patterns that repeat more often than expected by chance (Beggs and Plenz, 2004). The figure shows several such patterns from an acute cortical slice. These patterns are reproducible over periods of as long as 10 hours, and have a temporal precision of 4 ms (Beggs and Plenz, 2004). The stability and precision of these patterns suggest that neuronal avalanches could be used by [[neural networks]] as a substrate for storing information. In this sense, avalanches appear to be similar to sequences of action potentials observed in vivo while animals perform cognitive tasks. It is unclear at present whether the repeating activity patterns from in vivo data are also avalanches.  

While avalanches in [[critical sandpile models]] are stochastic in the patterns they form, avalanches of [[local field potentials]] occur in spatio-temporal patterns that repeat more often than expected by chance (Beggs and Plenz, 2004). The figure shows several such patterns from an acute cortical slice. These patterns are reproducible over periods of as long as 10 hours, and have a temporal precision of 4 ms (Beggs and Plenz, 2004). The stability and precision of these patterns suggest that neuronal avalanches could be used by [[neural networks]] as a substrate for storing information. In this sense, avalanches appear to be similar to sequences of action potentials observed in vivo while animals perform cognitive tasks. It is unclear at present whether the repeating activity patterns from in vivo data are also avalanches.

===Generality===

===Generality===