Monasson R, Rosay S
Laboratoire de Physique Théorique de l'ENS, CNRS & UPMC, 24 rue Lhomond, 75005 Paris, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Jun;87(6):062813. doi: 10.1103/PhysRevE.87.062813. Epub 2013 Jun 20.
We study the stable phases of an attractor neural network model, with binary units, for hippocampal place cells encoding one-dimensional (1D) or 2D spatial maps or environments. Different maps correspond to random allocations (permutations) of the place fields. Based on replica calculations we show that, below critical levels for the noise in the neural response and for the number of environments, the network activity is spatially localized in one environment. For high noise and loads the network activity extends over space, either uniformly or with spatial heterogeneities due to the crosstalk between the maps, and memory of environments is lost. Remarkably the spatially localized regime is very robust against the neural noise until it reaches its critical level. Numerical simulations are in excellent quantitative agreement with our theoretical predictions.
我们研究了一种具有二进制单元的吸引子神经网络模型的稳定相，该模型用于海马体位置细胞对一维（1D）或二维（2D）空间地图或环境进行编码。不同的地图对应于位置野的随机分配（排列）。基于副本计算，我们表明，在神经响应中的噪声和环境数量低于临界水平时，网络活动在一个环境中是空间局部化的。对于高噪声和高负载，网络活动会在空间上扩展，要么均匀扩展，要么由于地图之间的串扰而具有空间异质性，并且环境记忆会丢失。值得注意的是，空间局部化状态对神经噪声非常鲁棒，直到达到其临界水平。数值模拟与我们的理论预测在定量上非常吻合。
