论文标题
加权图形的边缘理想的符号能力的属性
Properties of symbolic powers of edge ideals of weighted oriented graphs
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
Let $D$ be a weighted oriented graph and $I(D)$ be its edge ideal. We provide one method to find all the minimal generators of $ I_{\subseteq C} $, where $ C $ is a maximal strong vertex cover of $D$ and $ I_{\subseteq C} $ is the intersections of irreducible ideals associated to the strong vertex covers contained in $C$. If $ D^{\prime} $ is an induced digraph of $D$, under certain condition on the strong vertex covers of $ D^{\prime} $ and $D$, we show that $ {I(D^{\prime})}^{(s)} \neq {I(D^{\prime})}^s $ for some $s \geq 2$ implies $ {I(D)}^{(s)} \neq {I(D)}^s $. We characterize all the maximal strong vertex covers of $D$ such that at most one edge is oriented into each of its vertex and $w(x) \geq 2$ if $°_D(x)\geq 2 $ for all $x \in V(D)$. If $ D $ is a weighted rooted tree with degree of root is $ 1 $ and $ w(x) \geq 2 $ when $ °_D(x) \geq 2 $ for all $ x \in V(D) $, we show that $ {I(D)}^{(s)} = {I(D)}^s $ for all $s \geq 2$
