The aim of this primer is to introduce the subject of knowledge engineering
in a concise but synthetic way to develop the reader's intuition about the
area.

本文旨在从简洁且综合的方式介绍知识工程学科，以发展读者对该领域的直觉。

知识工程入门

A Knowledge Engineering Primer

Take N sites distributed randomly and uniformly on a smooth closed surface.
We express the expected distance <D_k(N)> from an arbitrary point on the
surface to its kth-nearest neighboring site, in terms of the function A(l)
giving the area of a disc of radius l about that point. We then find two
universalities. First, for a flat surface, where A(l)=\pi l^2, the k-dependence
and the N-dependence separate in <D_k(N)>. All kth-nearest neighbor distances
thus have the same scaling law in N. Second, for a curved surface, the average
\int <D_k(N)> d\mu over the surface is a topological invariant at leading and
subleading order in a large N expansion. The 1/N scaling series then depends,
up through O(1/N), only on the surface's topology and not on its precise shape.
We discuss the case of higher dimensions (d>2), and also interpret our results
using Regge calculus.

本文研究了平面和曲面上的最近邻距离，发现对于平面上的情况，最近邻距离的依赖于 k 和 N 是分离的；对于曲面的情况，平均最近邻距离是拓扑不变量，且与曲面的具体形状无关，文中也研究了高维情况，并使用 Regge calculus 进行了解释。