부산대학교 도서관

The article under discussion, titled "Climbing Escher's stairs: A way to approximate stability landscapes in multidimensional systems" (doi: 10.1371/journal.pcbi.1007788), has captured our attention due to important methodological limitations that we believe warrant discussion. Our aim in writing this Formal Comment is to bring to the attention of potential readers and users the following key points: 1. The construction of the potential landscape function necessitates the global integrability of the velocity functions. However, the decomposition method outlined in this article is only applied to the Jacobian of the velocity functions instead of the velocity functions themselves, which leads to path-dependent integrals. Such a characteristic is not desirable for a potential landscape function. 2. In the article's implementation, integration is conducted along the x- and y-axes. This approach renders the decomposition method, which primarily affects the non-diagonal elements in the Jacobian matrix, ineffective. 3. We provide evidence that removing the core step of the method, the decomposition process, in the rolldown package (now renamed as waydown), results in identical output. This finding highlights the ineffectiveness of this crucial implementation step. 4. In our Comment, we also offer recommendations for potential alternatives for readers interested in constructing potential landscape functions.