论文标题
部分可观测时空混沌系统的无模型预测
On The Scale Dependence and Spacetime Dimension of the Internet with Causal Sets
论文作者
论文摘要
使用统计尺寸的统计度量测量来计算Internet和其他图形的有效平均空间维度，该尺寸基于起点集合的键入边缘（链接）。该方法应用于CAIDA的ITDK数据。使用低尺寸高管将不同尺度的有效尺寸校准到常规的欧几里德尺寸。 Internet时空具有“泡沫”多尺度遏制层次结构，具有相互交织的语义类型。在设备节点频谱中有一个紧急尺度，可在设备节点频谱中进行大致远距离顺序，但是在AS级别（存在有限距离遏制的情况下，这并不明显。因此，统计维度是一个局部变化的度量，它依赖于规模，为Kaluza-Klein理论的隐藏规模依赖性维度提供了视觉类比。 Internet的特征外部维度位于1.66 +-0.00和6.12 +-0.00之间，最大内部维度上升到7.7。
A statistical measure of dimension is used to compute the effective average space dimension for the Internet and other graphs, based on typed edges (links) from an ensemble of starting points. The method is applied to CAIDA's ITDK data for the Internet. The effective dimension at different scales is calibrated to the conventional Euclidean dimension using low dimensional hypercubes. Internet spacetime has a 'foamy' multi-scale containment hierarchy, with interleaving semantic types. There is an emergent scale for approximate long range order in the device node spectrum, but this is not evident at the AS level, where there is finite distance containment. Statistical dimension is thus a locally varying measure, which is scale-dependent, giving an visual analogy for the hidden scale-dependent dimensions of Kaluza-Klein theories. The characteristic exterior dimensions of the Internet lie between 1.66 +- 0.00 and 6.12 +- 0.00, and maximal interior dimensions rise to 7.7.
