A SPECTRAL METHOD FOR AGGREGATING VARIABLES IN LINEAR DYNAMICAL SYSTEMS WITH APPLICATION TO CELLULAR AUTOMATA RENORMALIZATION
A SPECTRAL METHOD FOR AGGREGATING VARIABLES IN LINEAR DYNAMICAL SYSTEMS WITH APPLICATION TO CELLULAR AUTOMATA RENORMALIZATION
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DOI：
10.1142/s0219525909002155
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发表时间：
2009-04-01
影响因子：
0.4
通讯作者：
Gornerup, Olof
中科院分区：
文献类型：
--
作者：
Jacobi, Martin Nilsson;Gornerup, Olof
我们提出了一种通过线性动力系统中变量或状态的聚合来识别粗粒度动力学的方法。聚合条件表示为定义动力学的矩阵的对偶特征向量集的置换对称。通过三种不同类型的可约马尔可夫链的例子说明了该条件的适用性：由独立子系统组成的系统、具有对称性的动力学和近解耦马尔可夫链。此外，我们还展示了如何将该方法应用于粗粒度元胞自动机。
We present a method for identifying coarse-grained dynamics through aggregation of variables or states in linear dynamical systems. The condition for aggregation is expressed as a permutation symmetry of a set of dual eigenvectors of the matrix that defines the dynamics. The applicability of the condition is illustrated in examples from three different generic classes of reducible Markov chains: systems consisting of independent subsystems, dynamics with symmetries, and nearly decoupled Markov chains. Furthermore we show how the method can be used to coarse-grain cellular automata.