线性房室树模型的可辨识性及输入-输出方程的一般公式
Identifiability of linear compartmental tree models and a general formula for input-output equations
AI总结：
本文解决了底层图为双向树的线性房室模型（单输入单输出）的结构可辨识性问题，提出可通过视觉验证可辨识性，并给出输入-输出方程系数的一般公式及模型扩充下可辨识性的保持条件。
摘要：
线性房室模型理论中的一个基础问题是，如何直接从模型的组合结构来评估一个模型是否具有结构可辨识性——即参数值能否从无噪声数据中推断出来。我们的主要结果针对底层图为双向树的模型（具有一个输入和一个输出）完整回答了这一问题；此外，这类模型的可辨识性可以通过视觉验证。这种结构的模型包括在生物应用中经常出现的两个模型族：链状和乳腺状模型。我们对这类模型的分析得益于两项辅助结果，它们本身也具有重要意义。一项结果首次给出了输入-输出方程（可用于确定可辨识性的某些方程）系数的一般公式，允许输入和输出位于不同的房室。在另一项辅助结果中，我们证明了当模型以特定方式被扩大和改变时，可辨识性得以保持，这些方式涉及向现有房室添加带有双向边的新房室。
英文摘要：
A foundational question in the theory of linear compartmental models is how to assess whether a model is structurally identifiable -- that is, whether parameter values can be inferred from noiseless data -- directly from the combinatorics of the model. Our main result completely answers this question for models (with one input and one output) in which the underlying graph is a bidirectional tree; moreover, identifiability of such models can be verified visually}. Models of this structure include two families of models often appearing in biological applications: catenary and mammillary models. Our analysis of such models is enabled by two supporting results, which are significant in their own right. One result gives the first general formula for the coefficients of input-output equations (certain equations that can be used to determine identifiability) that allows for input and output to be in distinct compartments}. In another supporting result, we prove that identifiability is preserved when a model is enlarged and altered in specific ways involving adding a new compartment with a bidirected edge to an existing compartment.
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