论文标题
连锁综合体的局部一致性
Local congruence of chain complexes
论文作者
论文摘要
本文的目的是使用单元格的一致性将一组局部链复合物转换为单个全局复合物，从拓扑上求解浮点算术的数值不准确性。在计算由蜂窝复合物集合产生的空间布置时，一个人可能是从独立有效地计算每个单个输入2细胞与其他单一输入的相交开始的。这些交叉路口的拓扑结构在一组（0-2）维链复合物中进行了整理。本文的目标是通过使用0-，1-和2细胞（基本链）之间的等效关系来合并局部链。特别是，我们将块 - 二基因共核矩阵[Δ_0]和[Δ_1]降低，用作局部链链的矩阵累加因子，将全球矩阵[Δ_0]和[Δ_1]和[Δ_1]和[Δ_1]，一致性代表的代表，i.e.e.e.e.e.e.e.e.e.e.e.e.e.e.e.e.e.e. i i.e equluence in equante colkune corke element element element element element element all 0-1--1-- 2-cells vivi。该算法使用Suitesparse：Graphblas标准的Graphblas实现的Julia端口进行了编码，该算法是使用线性代数和稀疏矩阵在大图上有效计算算法的，并构想了[1，2]。
The object of this paper is to transform a set of local chain complexes to a single global complex using an equivalence relation of congruence of cells, solving topologically the numerical inaccuracies of floating-point arithmetics. While computing the space arrangement generated by a collection of cellular complexes, one may start from independently and efficiently computing the intersection of each single input 2-cell with the others. The topology of these intersections is codified within a set of (0-2)-dimensional chain complexes. The target of this paper is to merge the local chains by using the equivalence relations of ε-congruence between 0-, 1-, and 2-cells (elementary chains). In particular, we reduce the block-diagonal coboundary matrices [Δ_0] and [Δ_1], used as matrix accumulators of the local coboundary chains, to the global matrices [δ_0] and [δ_1], representative of congruence topology, i.e., of congruence quotients between all 0-,1-,2-cells, via elementary algebraic operations on their columns. This algorithm is codified using the Julia porting of the SuiteSparse:GraphBLAS implementation of the GraphBLAS standard, conceived to efficiently compute algorithms on large graphs using linear algebra and sparse matrices [1, 2].
