论文标题
四个立方体
Four Cubes
论文作者
论文摘要
提出了对$ \ {0，1 \}^n $ boolean空间中构建的四个图的属性的简短调查。根据丑陋的小鸭定理，定义了稀疏分布式记忆模型中人造神经元的柔性激活功能。 $ n $ -cube的2-FACE三角剖分的Cotan Laplacian具有对应于$ \ {0，1 \}^n $ space的锤距距离分布的eigenvalues的归化频谱。 Degenerate spectrum of eigenvalues of the cotan Laplacian defined on the graph comprising $2^n$ 2-face triangulated $n$-cubes sharing common origin includes all integers from 0 to 3$n$, without the eigenvalue of 3$n$-1 (multiplicities of the same eigenvalues form A038717 OEIS sequence), while the multiplicities of the same eigenvalues $ [ - n \ sqrt {2}，n \ sqrt {2}] $的$ 2^n $ -cube形式trinomial三角形的邻接矩阵。还讨论了该图的距离矩阵，提供了进一步的OEI序列及其与Buckminster Fuller Vector平衡的关系。
A short survey on the properties of four graphs constructed in $\{0, 1\}^n$ Boolean space is presented. Flexible activation function of an artificial neuron in a sparse distributed memory model is defined on the basis of the Ugly duckling theorem. Cotan Laplacian on 2-face triangulation of $n$-cube has degenerate spectrum of eigenvalues corresponding to the Hamming distance distribution of $\{0, 1\}^n$ space. Degenerate spectrum of eigenvalues of the cotan Laplacian defined on the graph comprising $2^n$ 2-face triangulated $n$-cubes sharing common origin includes all integers from 0 to 3$n$, without the eigenvalue of 3$n$-1 (multiplicities of the same eigenvalues form A038717 OEIS sequence), while the multiplicities of the same eigenvalues $[-n\sqrt{2}, n\sqrt{2}]$ of the adjacency matrix of $2^n$-cube form trinomial triangle. The distance matrix of this graph, providing further OEIS sequences, as well as its relation with Buckminster Fuller vector equilibrium is also discussed.
