arXiv subjects

Shiruo Wang

Publications and source records attributed to Shiruo Wang.

3 recordsLinked to original sources

arXiv2026

A statistical theory of graph regularization for RNA velocity near developmental bifurcations

Graph-based regularization is widely used to stabilize noisy RNA-velocity estimates by encouraging transcriptionally similar cells to share similar velocity vectors. Near developmental bifurcations, however, proximity-based graphs may connect cells from distinct daughter lineages, reducing estimation variance at the cost of attenuating biologically meaningful lineage-specific dynamics. We formulate graph-regularized RNA velocity as a statistical estimation problem on a potentially misspecified cell-state graph and develop a theoretical framework for analyzing this trade-off. We derive an exact graph-spectral bias--variance decomposition that characterizes how Laplacian regularization suppresses estimation noise while introducing systematic smoothing bias. To quantify lineage preservation, we introduce a branch-sensitive risk that separates within-lineage denoising from cross-lineage information leakage. We further show that persistent cross-branch connectivity can induce nonvanishing branch bias, implying that standard proximity-graph regularization may remain asymptotically inconsistent near developmental bifurcations. These results provide a mathematical foundation for understanding both the statistical benefits and the geometric limitations of graph regularization for RNA-velocity estimation.

math.ST↗

arXiv2026

Decoding gene regulatory networks from single-cell RNA velocity

We formulate gene regulatory network reconstruction from RNA velocity as a sparse dynamical inverse problem. We show that control-only data can be structurally nonidentifying and characterize excitation conditions under which controlled perturbations restore identifiability by generating complementary regulator trajectories. To enable stable reconstruction from noisy data, we develop an integral sparse estimator that avoids numerical differentiation and derive recovery bounds separating stochastic error from systematic contributions due to latent-time uncertainty, kinetic-parameter error, numerical quadrature, and model misspecification. Synthetic experiments illustrate perturbation-assisted identifiability, improved conditioning, and the robustness of integral reconstruction. Applied to perturbation-resolved RPE1 RNA-velocity data, the framework yields an empirically full-rank design whose conditioning improves with perturbational diversity and a reconstructed network core stable under perturbation subsampling. Held-out evaluation further shows that identifiability and reconstruction stability do not imply uniform predictive improvement. These results connect perturbational excitation, identifiability, and stable sparse recovery in regulatory dynamical systems.

math.DS↗

arXiv2025

Genus Stability of $\mathbb Z_p^\times$-Towers

Let $p$ be a prime. Consider a tower of smooth projective geometrically irreducible curves over $\mathbb F_p$, $\mathscr C:\cdots\rightarrow C_n\rightarrow\cdots\rightarrow C_1\rightarrow C_0=\mathbb P^1$ whose Galois group is isomorphic to $\mathbb Z_p^\times$. In this paper, we study genus growth of the tower $\mathscr C$ and determine all the $\mathbb Z_p^\times$-towers with genus be a quadratic equation of $p^{n}$ when $n$ is sufficiently large.

math.NT↗