论文标题
心理物理学的物理学：尖峰神经元的两个耦合方晶格在关键时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
论文作者
论文摘要
心理物理学试图将物理输入幅度与心理或神经相关性联系起来。从统计物理学的意义上讲，要考虑宏观心理物理定律的微观模型几乎是未开发的领域。在这里，我们检查了一个由随机整合和开火细胞的两个连接的平方晶格组成的感觉上皮。使用一个方格晶格，我们获得了史蒂文斯法律$ρ\ propto h^m $，史蒂文斯的指数$ m = 0.254 $和一个sigmoidal饱和度，其中$ρ$是神经元网络活动，$ h $是输入强度（外部字段）。我们将史蒂文斯的权力定律指数与临界指数相关联，为$ m = 1/Δ_h=β/σ$。我们还表明，该系统与定向渗透（DP）通用类（或Compact-DP类）有关。在堆叠的两层平方晶格以及第一层和第二层之间的连接性一小部分时，我们在输出层$ρ_2\ propto h^{m_2} $中获得，其中$ m_2 = 0.08 \ of m m^2 $，与一个巨大的动态范围相对应。仅当图层接近其临界点时，这种动态范围的增强才会发生。
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.
