论文标题
时间依赖的分支过程：振荡神经元雪崩的模型
Time-dependent branching processes: a model of oscillating neuronal avalanches
论文作者
论文摘要
最近，已经观察到神经元雪崩表现出振荡，这一现象被认为是无标度行为的共存（接近临界性的雪崩）和比例依赖性动力学（振荡）。具有恒定灭绝和分支速率的普通连续分支过程通常用作神经元活动的模型，但它们缺乏任何这种时间依赖性。在目前的工作中，我们通过允许灭绝速率及时振荡作为描述皮质动力学的新模型来扩展基本的分支过程。通过扰动场理论，我们以封闭形式得出相关的可观察物。我们通过与数字和定性比较与可用实验结果进行定性比较来支持我们的发现。
Recently, neuronal avalanches have been observed to display oscillations, a phenomenon regarded as the co-existence of a scale-free behaviour (the avalanches close to criticality) and scale-dependent dynamics (the oscillations). Ordinary continuous-time branching processes with constant extinction and branching rates are commonly used as models of neuronal activity, yet they lack any such time-dependence. In the present work, we extend a basic branching process by allowing the extinction rate to oscillate in time as a new model to describe cortical dynamics. By means of a perturbative field theory, we derive relevant observables in closed form. We support our findings by quantative comparison to numerics and qualitative comparison to available experimental results.
