论文标题
离散动态系统的代数网络重建
Algebraic network reconstruction of discrete dynamical systems
论文作者
论文摘要
我们提出了一种计算代数解决方案，可以从数据中逆转离散动力系统的网络结构。我们使用单一理想来确定变量之间的依赖关系，这些变量对生成离散时间，连续空间数据的过程的可能接线图进行了编码约束。我们的工作假设每个变量要么单调增加或减小。我们证明，借助足够的数据，即使在存在小噪声的情况下，我们的方法也可以重建正确的唯一接线图。
We present a computational algebra solution to reverse engineering the network structure of discrete dynamical systems from data. We use monomial ideals to determine dependencies between variables that encode constraints on the possible wiring diagrams underlying the process generating the discrete-time, continuous-space data. Our work assumes that each variable is either monotone increasing or decreasing. We prove that with enough data, even in the presence of small noise, our method can reconstruct the correct unique wiring diagram.
