心理物理学的物理学：两个耦合的尖峰神经元正方形晶格在临界状态下具有巨大的动态范围
Physics of Psychophysics: two coupled square lattices of spiking neurons have huge dynamic range at criticality
摘要：
心理物理学试图将物理输入的大小与心理或神经相关物联系起来。从统计物理学的意义上讲，解释宏观心理物理学定律的微观模型是一个几乎未被探索的领域。在这里，我们研究了由两个连接的随机整合和火灾细胞的正方形格子组成的感觉上皮。对于一个正方形格子，我们得到具有史蒂文斯指数$m = 0.254$和S形饱和度的史蒂文斯定律$ρ\propto h^m$，其中$ρ$是神经元网络活动，$h$是输入强度（外场）。我们将Stevens幂律指数与场临界指数联系起来，表示为$m = 1/δ_h = β/σ$。我们还表明，该系统属于定向渗流（DP）的普适性类（或可能的紧凑DP类）。利用堆叠的两层正方形晶格，以及第一层和第二层之间的一部分连接，我们在输出层获得$ρ_ 2 \propto h^{m_2}$和$m_2 = 0.08 \approx m^2$，其对应于巨大的动态范围。动态范围的这种增强仅在层接近其临界点时发生。
英文摘要：
Psychophysics try to relate physical input magnitudes to psychological or neural correlates. Microscopic models to account for macroscopic psychophysical laws, in the sense of statistical physics, are an almost unexplored area. Here we examine a sensory epithelium composed of two connected square lattices of stochastic integrate-and-fire cells. With one square lattice we obtain a Stevens's law $ρ\propto h^m$ with Stevens's exponent $m = 0.254$ and a sigmoidal saturation, where $ρ$ is the neuronal network activity and $h$ is the input intensity (external field). We relate Stevens's power law exponent with the field critical exponent as $m = 1/δ_h = β/σ$. We also show that this system pertains to the Directed Percolation (DP) universality class (or perhaps the Compact-DP class). With stacked two layers of square lattices, and a fraction of connectivity between the first and second layer, we obtain at the output layer $ρ_ 2 \propto h^{m_2}$, with $m_2 = 0.08 \approx m^2$, which corresponds to a huge dynamic range. This enhancement of the dynamic range only occurs when the layers are close to their critical point.
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