发表机构
Sejong University（世宗大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对感觉适应场景，揭示低阶系统辨识会定性失效，明确了自适应系统降阶的极点边界特性及随机可辨识性相关规律，为评估生物自适应低维模型局限性提供了框架。
AI 中文摘要
感觉适应为低阶系统辨识可能出现定性失效提供了具体场景。我们证明，一个由全部实一阶弛豫模式构成的固定高阶自适应系统，可被约化至二阶极点边界的两侧：低频矩匹配给出ρ_矩=4.50，而有限窗口拟合给出ρ_窗口=3.31，且推断出的极点类别会随采样协议进一步变化。因此，约化模型的实-复分类本身不具有降阶不变性。随后，我们利用通用两态谱将随机可辨识性与适应关联：对于非平凡耦合和单态观测，当隐藏态无自弛豫时，交叉扩散会从标量谱中消失。在自适应模型中，该条件恰好是产生精确适应的积分记忆极限，而泄漏记忆则恢复谱敏感性。对于精确适应模型，高斯路径空间不可逆性仍依赖于隐藏交叉扩散通道，因此{H,S_x}不决定不可逆率。此外，对于指定的全偶约化两态漂移且ρ<4，仅漂移的下界为σ≥τ_x⁻¹(4/ρ-1)。已发表的大肠杆菌和秀丽隐杆线虫响应为这些极限提供了生物学实例。本文确立的传递函数不变量、降阶相关性质与隐藏态量之间的区分，为评估自适应生物动力学低维模型的局限性提供了具体框架。
英文摘要
Sensory adaptation provides a concrete setting in which low-order system identification can fail qualitatively. We show that one fixed higher-order adaptive system composed entirely of real first-order relaxation modes can be reduced to opposite sides of the second-order pole boundary: low-frequency moment matching gives $ρ_{\rm moment}=4.50$, whereas finite-window fitting gives $ρ_{\rm window}=3.31$, and the inferred pole class changes further with sampling protocol. Thus the real-versus-complex classification of a reduced model is not itself reduction invariant. We then use the general two-state spectrum to connect stochastic identifiability to adaptation: for nontrivial coupling and one-state observation, cross diffusion drops out of the scalar spectrum when the hidden state has no self-relaxation. In the adaptive model, this condition is precisely the integral-memory limit that produces exact adaptation, while leaky memory restores spectral sensitivity. For the exact-adaptation model, the Gaussian path-space irreversibility nevertheless depends on the hidden cross-diffusion channel. Hence $\{H,S_x\}$ does not determine the irreversibility rate. Independently, for a specified all-even reduced two-state drift with $ρ<4$, the drift-only lower bound is $σ\ge τ_x^{-1}(4/ρ-1)$. Published \textit{E.~coli} and \textit{C.~elegans} responses provide biological examples of these limits. The distinction established here between transfer-function invariants, reduction-dependent properties, and hidden-state quantities provides a concrete framework for evaluating the limitations of low-dimensional models of adaptive biological dynamics.
Comments9 pages and 5 figures
