Identifiability of Linear Compartmental Models: The Impact of Removing Leaks and Edges

房室模型的结构可辨识性：近期进展与未来方向

Structural Identifiability of Compartmental Models: Recent Progress and Future Directions

本文综述房室模型结构可辨识性的理论与应用进展，涵盖流行病学、肿瘤学等领域的可辨识性分析、不可辨识模型的重参数化方法及从结构预测可辨识性的算法成果，并展望未来研究方向。

Identifiability of Linear Compartmental Models: The Effect of Moving Inputs, Outputs, and Leaks

A mathematical model is identifiable if its parameters can be recovered from data. Here we investigate, for linear compartmental models, whether (local, generic) identifiability is preserved when parts of the model -- specifically, inputs, outputs, leaks, and edges -- are moved, added, or deleted. Our results are as follows. First, for certain catenary, cycle, and mammillary models, moving or deleting the leak preserves identifiability. Next, for cycle models with up to one leak, moving inputs or outputs preserves identifiability. Thus, every cycle model with up to one leak (and at least one i…

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

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。

Linear compartmental models: input-output equations and operations that preserve identifiability

This work focuses on the question of how identifiability of a mathematical model, that is, whether parameters can be recovered from data, is related to identifiability of its submodels. We look specifically at linear compartmental models and investigate when identifiability is preserved after adding or removing model components. In particular, we examine whether identifiability is preserved when an input, output, edge, or leak is added or deleted. Our approach, via differential algebra, is to analyze specific input-output equations of a model and the Jacobian of the associated coefficient map.…

Identifiability of linear compartmental models: the singular locus

This work addresses the problem of identifiability, that is, the question of whether parameters can be recovered from data, for linear compartmental models. Using standard differential algebra techniques, the question of whether a given model is generically locally identifiable is equivalent to asking whether the Jacobian matrix of a certain coefficient map, arising from input-output equations, is generically full rank. A natural next step is to study the set of parameter values where the Jacobian matrix drops in rank, which we refer to as the locus of non-identifiable parameter values, or, fo…

有向环与链状线性房室模型的可辨识性

Identifiability of directed-cycle and catenary linear compartment models

本文研究有向环与链状线性房室模型的结构可辨识性，完整刻画了所有参数一般局部可辨识的有向环模型，并给出链状模型的输入-输出方程公式。