| − | Power law distributions of event sizes are often seen in complex phenomena including earthquakes, [[phase transitions]], [[percolation]], forest fires, financial market fluctuations, avalanches in the [[game of life]] and a host of others (Bak, 1996). In some specific cases, this similarity appears to be more than superficial. For example, earthquake models incorporate local rules in which forces at one site are distributed to nearest neighbors without dissipation. This conservation of forces is similar to the conservation of probabilities in the critical branching model described above. This suggests that conservation of synaptic strengths, as reported in (Royer and Pare, 2003) could be a mechanism responsible for maintaining a network near the critical point. In a related idea, simulations indicate that networks can be kept nearly critical when the total sum of synaptic strengths hovers near a constant value (Hsu and Beggs, 2006). This could be accomplished through a mechanism like synaptic scaling (Turrigiano and Nelson, 2000), which has been observed experimentally. Finally, recently "burned" areas in forest fire models are refractory, while unburned areas are more likely to ignite. This balance of refractoriness and excitability combine to maintain the system near the critical point. Recent models of neuronal avalanches (Levina, Herrmann and Geisel, 2005) have suggested that short-term synaptic depression and facilitation may also serve to drive neuronal networks toward the critical point where avalanches occur. Thus, an understanding of power laws in diverse complex systems can suggest mechanisms that might underlie criticality in neuronal networks.
| + | 事件大小的幂律分布通常出现在复杂的现象中，包括地震、[[相变]]、[[渗流]]、森林火灾、金融市场波动、[[生命游戏]]中的雪崩以及其他许多现象（Bak，1996）。在某些特定情况下，这种相似性似乎不仅仅是表面的。例如，地震模型结合了局部规则，其中一个地点的力被分配到最近的邻居，而没有消散。这种力守恒类似于上述临界分支模型中的概率守恒。这表明（Royer和Pare，2003）中报告的突触强度守恒可能是维持临界点附近网络的机制。在一个相关的想法中，模拟表明，当突触强度的总和徘徊在一个恒定值附近时，网络可以几乎保持临界（Hsu和Beggs，2006）。这可能是通过像突触缩放这样的机制来实现的（Turrigiano和Nelson，2000），并已经在实验中观察到了。最后，森林火灾模型中最近“燃烧”的区域是耐火的，而未燃烧的区域更容易着火。耐火性和兴奋性的这种平衡结合在一起，使系统保持在临界点附近。最近的神经雪崩模型（Levina、Herrmann和Geisel，2005）表明，短期突触抑制和促进也可能有助于推动神经元网络走向雪崩发生的临界点。因此，了解不同复杂系统中的幂律可以提出可能构成神经网络临界性基础的机制。 |
| − | A simple electronic model of avalanche generation consists of a two-dimensional array of neon lamps, each one connected to a resistor towards a global DC control voltage and capacitively coupled to its von Neumann neighbors. Neon lamps possess rich dynamical properties: as the applied voltage changes, the transition between the "on" and "off" phases is at the same time significantly hysteretic and stochastic (Dance, 1968). The system displays two phases, <math>I</math> and <math>II</math>, respectively characterized by low and high event rate and spatiotemporal order: the transition between them is strongly hysteretic, hence unequivocally first-order. Nevertheless, close to the spinal point of the <math>I\rightarrow II</math> transition, critical precursors emerge in the form of avalanches (Fig. 8) having the same scaling exponents characterizing neural activity, namely <math>\alpha\approx3/2</math> for size and <math>\alpha\approx2</math> for duration (Minati et al., 2016).
| + | 雪崩产生的一个简单电子模型由一个二维霓虹灯阵列组成，每个霓虹灯连接到一个朝向全局直流控制电压的电阻器，并电容耦合到其冯·诺依曼邻居。霓虹灯具有丰富的动态特性：随着外加电压的变化，"开 "和 "关 "阶段之间的转换同时具有明显的滞后性和随机性（Dance，1968）。该系统显示两个阶段，<math>I</math>和<math>II</math>，分别具有低和高事件率和时空顺序的特征：它们之间的过渡是强滞后的，因此明确为一阶。然而，在接近<math>I\rightarrow II</math>转换的脊柱点时，关键前驱体以雪崩的形式出现（图8），具有相同的表征神经活动的标度指数，即大小为<math>\alpha\approx3/2</math>，持续时间为<math>\alpha\approx2</math>（Minati等人，2016）。 |