论文标题
渗漏的尖峰神经元的随机系统的亚竞争力
Metastability in a Stochastic System of Spiking Neurons with Leakage
论文作者
论文摘要
我们考虑了一个有限的相互作用点过程系统，该系统与可变长度的内存建模有限但大的尖峰神经元网络具有两个不同的泄漏机制。与每个神经元相关联，有两个点过程，描述了其连续的尖峰和泄漏时间。对于每个神经元，尖峰点过程的速率是其膜电位的指数函数，其限制是，当膜电位为0时，速率为0。在每个尖峰时间，神经元的膜电位重置为0，并且同时将其他神经元的膜电位增加一个单位。泄漏可以通过两种不同的方式进行建模。首先，在与神经元相关的泄漏点过程的每个发生时间，该神经元的膜电位重置为0，对其他神经元没有影响。在第二个方面，如果神经元的膜电位严格为阳性，则在与该神经元相关的泄漏点过程的每个发生时间，其膜电位会降低一个单位，而对其他神经元无影响。在这两种情况下，神经元的泄漏点过程都有恒定的速率。对于这两种模型，我们都证明该系统具有亚稳定的行为，因为人口大小发散。这意味着系统被零膜电位列表捕获的时间适当地缩放为平均一个指数随机时间。
We consider a finite system of interacting point processes with memory of variable length modeling a finite but large network of spiking neurons with two different leakage mechanisms. Associated to each neuron there are two point processes, describing its successive spiking and leakage times. For each neuron, the rate of the spiking point process is an exponential function of its membrane potential, with the restriction that the rate takes the value 0 when the membrane potential is 0. At each spiking time, the membrane potential of the neuron resets to 0, and simultaneously, the membrane potentials of the other neurons increase by one unit. The leakage can be modeled in two different ways. In the first way, at each occurrence time of the leakage point process associated to a neuron, the membrane potential of that neuron is reset to 0, with no effect on the other neurons. In the second way, if the membrane potential of the neuron is strictly positive, at each occurrence time of the leakage point process associated to that neuron, its membrane potential decreases by one unit, with no effect on the other neurons. In both cases, the leakage point process of the neurons has constant rate. For both models, we prove that the system has a metastable behavior as the population size diverges. This means that the time at which the system gets trapped by the list of null membrane potentials suitably re-scaled converges to a mean one exponential random time.
