The core issue is as follows: Some core datasets for studying cell differentiation can be downloaded from the relevant links in scvelo. I have always wanted to use the Waddington landscape to represent the process of cell differentiation, which is indeed a mainstream approach in the biological community. However, I have found that there are actually many problems in snapshot data such as single-cell transcriptome data. My previous core viewpoint was v(x) = -dU(x) + F(x), where conservative force non-conservative force (potential gradient) (cell cycle, etc.). In reality, the data you actually obtain is often multi-branch, involving complex processes such as the cell cycle. Moreover, it is impossible to have explicit time labels like methods that utilize optimal transport. I initially wanted to use the concept of pseudo-time to represent the process of cell differentiation, but I found that this depends on the quality of the root cell selection. I believe there are corresponding methods to address this point. The core is that the actual differentiation process is multi-branch, and pseudo-time will be forced to undergo compression and transformation. Methods such as DPT, Palantir, and Page aim to obtain global topological properties, often focusing on the so-called diffusion distance. Secondly, pseudo-time loses its constraint on differentiation branches at bifurcation points. Furthermore, I want to use the Poisson potential obtained by ddhodge (also a relevant indicator of diffusion distance). How can I obtain a global, unified, and branch-handling pseudo-time, or customize other indicators.

Pseudo-time poses a problem, and the core issue lies in the equation v(x) = -dU(x) + F(x), where v(x) cannot be simply represented by RNA-velocity. I believe that the calculation of RNA velocity is often conducted at the gene space level. My core focus is on constructing a landscape in waddingtong, which is often visualized in 2D or in PCA space. The gene space level is convenient for downstream tasks, but in reality, it is very difficult to form a unified global landscape. Therefore, it involves embedding RNA velocity in a low-dimensional space. I believe that once these tools are projected into PCA space, many so-called indicators, such as CBDir and ICooh, cannot be utilized. This is because they are more or less overfitting the noise of high-dimensional RNA transcription rates, which becomes evident after dimensionality reduction, compression, and filtering. Secondly, there are no indicators for evaluating RNA velocity in a low-dimensional space, which is very challenging. I want to use global constraints to construct a landscape, and I also want to explain the process of cell differentiation from the perspective of energy and information. I feel that there are great difficulties, and there is no one to lead the way. The information on the internet is very one-sided and lacks systematicness. The answers provided by AI are not satisfactory, and the illusion rate is high. If there are experts who have conducted relevant analysis, could you please provide some help? Thank you all.

This is so specific, I doubt you will get help online. I would consider asking my PI to establish collaborations with people working on similar things, and be it only for some brainstorm meetings.