论文标题
过滤网络的统计信息
Filtering Statistics on Networks
论文作者
论文摘要
我们探讨了在许多确定性和随机图上过滤简单模式的统计信息，作为复杂系统中信息处理的可拖动简单示例。在此问题中，多个输入映射到相同的输出，并且过滤的统计数据由此退化的分布表示。对于环上的一些简单的过滤模式，我们获得了问题的精确解决方案，并描述了数值更困难的滤波器设置。对于每个过滤模式和网络，我们发现了几个数字基本上描述了过滤的统计信息，并比较了它们的不同网络。我们针对具有不同体系结构的网络的结果似乎是由两个因素确定的：图形结构是确定性的还是随机的，以及顶点程度。我们发现，在随机图中进行过滤产生的统计数据比确定性图中的统计数据要多得多。通过增加图形的程度来降低这种统计丰富度。
We explored the statistics of filtering of simple patterns on a number of deterministic and random graphs as a tractable simple example of information processing in complex systems. In this problem, multiple inputs map to the same output, and the statistics of filtering is represented by the distribution of this degeneracy. For a few simple filter patterns on a ring we obtained an exact solution of the problem and described numerically more difficult filter setups. For each of the filter patterns and networks we found a few numbers essentially describing the statistics of filtering and compared them for different networks. Our results for networks with diverse architectures appear to be essentially determined by two factors: whether the graphs structure is deterministic or random, and the vertex degree. We find that filtering in random graphs produces a much richer statistics than in deterministic graphs. This statistical richness is reduced by increasing the graph's degree.
