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此词条由神经动力学读书会词条梳理志愿者Spidey0o0Zheng翻译审校，未经专家审核，带来阅读不便，请见谅。

[[Image:图1 数据表示示意图.jpg|thumb|400px|right|数据表示的示意图。超过三个标准差的[[局部场电位]]（LFPs）用黑色方块表示。]]

[[Image:图1 数据表示示意图.jpg|thumb|400px|right|图1:数据表示的示意图。超过三个标准差的[[局部场电位]]（LFPs）用黑色方块表示。]]

[[Image:Beggs_avalanche_movie.gif|frame|right|急性皮层切片中的神经雪崩。]]

[[Image:Beggs_avalanche_movie.gif|frame|right|图2:急性皮层切片中的神经雪崩。]]

'''神经雪崩'''是[[神经元]]网络中的一连串[http://www.scholarpedia.org/article/Bursting 爆发性]活动，其大小分布可以用[[幂律分布 power law|幂律]]来近似，如[[沙堆模型|临界沙堆模型]]（Bak等人，1987）。神经雪崩见于培养的和急性皮质切片（Beggs和Plenz，2003；2004）。在这些新皮层切片中，活动的特点是持续几十毫秒的短暂爆发，中间有几秒钟的静止期。当用[http://www.scholarpedia.org/article/Multielectrode_array 多电极阵列]观察时，在爆发期间被驱动超过阈值的电极数量近似于幂律分布。虽然这种现象具有高度的稳定性和可重复性，但它与完整大脑中的生理过程的关系目前还不清楚。

'''神经雪崩'''是[[神经元]]网络中的一连串[http://www.scholarpedia.org/article/Bursting 爆发性]活动，其大小分布可以用[[幂律分布 power law|幂律]]来近似，如[[沙堆模型|临界沙堆模型]]（Bak等人，1987）。神经雪崩见于培养的和急性皮质切片（Beggs和Plenz，2003；2004）。在这些新皮层切片中，活动的特点是持续几十毫秒的短暂爆发，中间有几秒钟的静止期。当用[http://www.scholarpedia.org/article/Multielectrode_array 多电极阵列]观察时，在爆发期间被驱动超过阈值的电极数量近似于幂律分布。虽然这种现象具有高度的稳定性和可重复性，但它与完整大脑中的生理过程的关系目前还不清楚。

==实验观察 Experimental Observations==

==实验观察 Experimental Observations==

[[Image:雪崩示例.jpg|thumb|400px|right|Example of an avalanche. Seven frames are shown, where each frame represents activity on the electrode array during one 4 ms time step. An avalanche is a series of consecutively active frames that is preceded by and terminated by blank frames. Avalanche size is given by the total number of active electrodes. The avalanche shown here has a size of 9.]]

[[Image:雪崩示例.jpg|thumb|400px|right|图3:雪崩示例。显示了7个帧，其中每个帧代表电极阵列在一个4毫秒的时间布长中的活动。雪崩是一系列连续的活动帧，开始和结束均是空白帧。雪崩的大小是由活动电极的总数决定的。这里显示的雪崩的大小为9。]]

===幂律尺寸分布 Power law size distribution===

===幂律尺寸分布 Power law size distribution===

The example avalanche shown has a size of 9 because this is the total number of electrodes that were driven over threshold. Avalanche sizes are distributed in a manner that is nearly fit by a [[power law]]. Due to the limited number of electrodes in the array, the power law begins to bend downward in a cutoff well before the array size of 60. But for larger electrode arrays, the power law is seen to extend much further.  

The example avalanche shown has a size of 9 because this is the total number of electrodes that were driven over threshold. Avalanche sizes are distributed in a manner that is nearly fit by a [[power law]]. Due to the limited number of electrodes in the array, the power law begins to bend downward in a cutoff well before the array size of 60. But for larger electrode arrays, the power law is seen to extend much further.  

[[Image:雪崩尺寸分布.jpg|thumb|500px|right|Avalanche size distributions. A, Distribution of sizes from acute slice [[LFP]]s recorded with a 60 electrode array, plotted in log-log space. Actual data are shown in black, while the output of a [[Poisson model]] is shown in red. In the Poisson model, each electrode fires at the same rate as that seen in the actual data, but independently of all the other electrodes. Note the large difference between the two curves. The actual data follow a nearly straight line for sizes from 1- 35; after this point there is a cutoff induced by the electrode array size. The straight line is indicative of a power law, suggesting that the network is operating near the [[self-organized criticality|critical point]] (unpublished data recorded by W. Chen, C. Haldeman, S. Wang, A. Tang, J.M. Beggs). B, Avalanche size distribution for spikes can be approximated by a straight line over three orders of magnitude in probability, without a sharp cutoff as seen in panel A. Data were collected with a 512 electrode array from an acute cortical slice bathed in high potassium and zero magnesium (unpublished work of A. Litke, S. Sher, M. Grivich, D. Petrusca, S. Kachiguine, J.M. Beggs). Spikes were thresholded at -3 standard deviations and were not sorted. Data were binned at 1.2 ms to match the short interelectrode distance of 60 μm. Results similar to A and B are also obtained from cortical slice cultures recorded in culture medium.]]

[[Image:雪崩尺寸分布.jpg|thumb|500px|right|图4:雪崩尺寸分布。 A, Distribution of sizes from acute slice [[LFP]]s recorded with a 60 electrode array, plotted in log-log space. Actual data are shown in black, while the output of a [[Poisson model]] is shown in red. In the Poisson model, each electrode fires at the same rate as that seen in the actual data, but independently of all the other electrodes. Note the large difference between the two curves. The actual data follow a nearly straight line for sizes from 1- 35; after this point there is a cutoff induced by the electrode array size. The straight line is indicative of a power law, suggesting that the network is operating near the [[self-organized criticality|critical point]] (unpublished data recorded by W. Chen, C. Haldeman, S. Wang, A. Tang, J.M. Beggs). B, Avalanche size distribution for spikes can be approximated by a straight line over three orders of magnitude in probability, without a sharp cutoff as seen in panel A. Data were collected with a 512 electrode array from an acute cortical slice bathed in high potassium and zero magnesium (unpublished work of A. Litke, S. Sher, M. Grivich, D. Petrusca, S. Kachiguine, J.M. Beggs). Spikes were thresholded at -3 standard deviations and were not sorted. Data were binned at 1.2 ms to match the short interelectrode distance of 60 μm. Results similar to A and B are also obtained from cortical slice cultures recorded in culture medium.]]

The equation of a [[power law]] is:

[[幂律分布]]的公式是:

:<math>

:<math>

P(S)=kS^{-\alpha}\,

P(S)=kS^{-\alpha}\,

[[Image:急性切片的重复雪崩的家族.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:急性切片的重复雪崩的家族.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]].]]  

 

[[临界沙堆模型]]中的雪崩在其形成的模式中是随机的，与之相比，[[局部场电位]]的雪崩发生的时空模式比预期的偶然性更频繁（Beggs和Plenz，2004）。图中显示了一个急性皮层切片的几个这样的模式。这些模式在长达10个小时的时间内是可重复的，其时间精度为4ms（Beggs和Plenz，2004）。这些模式的稳定性和精确性表明，神经雪崩可以被[[神经网络]]用作存储信息的基底。在这个意义上，雪崩似乎与在动物执行认知任务时在体内观察到的动作电位序列相似。目前还不清楚体内数据的重复活动模式是否也是雪崩。

[[沙堆模型｜临界沙堆模型]]中的雪崩在其形成的模式中是随机的，与之相比，[[局部场电位]]的雪崩发生的时空模式比预期的偶然性更频繁（Beggs和Plenz，2004）。图中显示了一个急性皮层切片的几个这样的模式。这些模式在长达10个小时的时间内是可重复的，其时间精度为4ms（Beggs和Plenz，2004）。这些模式的稳定性和精确性表明，神经雪崩可以被[[神经网络]]用作存储信息的基底。在这个意义上，雪崩似乎与在动物执行认知任务时在体内观察到的动作电位序列相似。目前还不清楚体内数据的重复活动模式是否也是雪崩。

===Generality===

===Generality===