发表机构
University of Salzburg（萨尔茨堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究证明，从单快照的平稳二阶空间统计量（结构因子）可辨识线性反应-扩散系统的有向相互作用算子与扩散率矩阵（至全局时间重标度），并指出绝对时间尺度需外部时钟，为肿瘤-免疫组织的有向细胞相互作用恢复提供理论依据。
AI 中文摘要
一个具有多个相互作用群体的系统的单个空间快照捕获了位置，但没有捕获导致观测的潜在动力学。这项工作探讨了快照的平稳二阶空间统计量能揭示线性反应-扩散动力学模型结构的哪些信息，特别是其相互作用算子的成对有向条目。观测值是矩阵值结构因子 $S(k)$，作为扩散继承的波数 $\kappa=|k|^2$ 依赖性的单参数族。主要结果是，对于任意数量的相互作用群体，有向相互作用算子 $A$ 和扩散率矩阵 $D$ 在 $\{S(\kappa)\}$ 下通常可辨识，直至一个全局时间重标度。这些发现并不与已知界限以及最近的结果相矛盾，即空间观测数据仅确定底层图的马尔可夫等价类。在这项工作中，我们确定了消除这一障碍的物理假设。绝对时间尺度无法从任何样本大小的单个快照中辨识，需要外部时钟。对于肿瘤-免疫组织，结果表明，有向细胞-细胞相互作用原则上可从单个切片中恢复，方向不能从平均密度或协方差矩阵推断，但可从交叉谱和自谱的波数依赖性推断，并且基线切片确定相互作用结构但不确定绝对速率。
英文摘要
A single spatial snapshot of a system with multiple interacting populations captures positions but not the underlying dynamics that have led to the observation. This work asks what the stationary second-order spatial statistics of a snapshot can reveal about the structure of the linear reaction-diffusion dynamical model, and in particular about the pairwise directed entries of its interaction operator. The observation is the matrix-valued structure factor $S(k)$ as a one-parameter family in the diffusion-inherited dependence on the wavenumber $κ=|k|^2$. The main result is that the directed interaction operator $A$ and the diffusivity matrix $D$ are generically identifiable for any number of interacting populations from $\{S(κ)\}$ up to a single global time rescaling. The findings do not contradict known bounds and the recent result that spatial observational data only determine the Markov equivalence class of the underlying graph. In this work, we identify physical assumptions that lift this barrier. The absolute time scale is not identifiable from a single snapshot of any sample size and requires an external clock. For tumor-immune tissue, the results imply that directed cell-cell interactions are in principle recoverable from one section, that the direction cannot be inferred from the mean densities or a covariance matrix, but from the wavenumber dependence of the cross and autospectra, and that a baseline section determines the interaction structure but not the absolute rates.
