AI 中文总结
该研究针对n级前馈级联，精确分解了夹带增益，通过Michaelis-Menten级联验证得非恒定周期进料会降低平均终产物。
AI 中文摘要
我们研究夹带增益（GOE），即n级前馈级联（由稳定的一阶滤波器与静态非线性函数交替构成）在周期输入下的平均稳态输出，与相同均值的恒定输入下的稳态输出之间的差值。主要结果是将GOE精确分解为局部Jensen间隙的加权和，每个间隙量化非线性函数产生的均值偏移，权重为下游增量增益的乘积除以线性时间常数。我们给出该分解的Bregman散度解释，以及GOE的二阶小振幅表达式，将其分解为局部曲率、波动能量和差分增益。我们用Michaelis-Menten级联验证理论结果，表明任何非恒定周期进料都会严格降低平均终产物，相较于相同均值的恒定进料。
英文摘要
We consider the gain of entrainment (GOE)--the difference between the average steady-state output under a periodic input and the steady-state output under a constant input with the same mean--for an $n$-stage feedforward cascade of stable first-order filters interleaved with static nonlinearities. The main result is an exact decomposition of GOE as a weighted sum of local Jensen gaps, where each gap quantifies the mean shift generated by a nonlinearity, and each weight is a product of downstream incremental gains divided by linear time constants. We provide a Bregman-divergence interpretation of the decomposition, and a second-order small-amplitude of GOE separating local curvature, fluctuation energy, and differential gains. We demonstrate the theoretical results using a Michaelis-Menten cascade showing that any nonconstant periodic feeding strictly reduces the average terminal product relative to constant feeding with the same mean.
