Ralph Twum | Searcharxiv

arXiv2026

Duplicial sets, crossed $G$-sets and descent categories

The goal of this note is to show that the left $\chi$-coalgebra, which is an additional structure on one of the coefficients used in the construction of the cyclic operator for the cyclic sets that generalises the twisted nerve of a group by Loday is an instance of a general theory of left $\chi$-coalgebras. It is also shown that in the general case, the resulting cyclic operator requires that the other coefficient needs to be equipped with a crossed $G$-sets structure.

math.QA↗

arXiv2023

Point in polygon calculation using vector geometric methods with application to geospatial data

In this work, we designed algorithms for the point in polygon problem based on the ray casting algorithm using equations from vector geometry. The algorithms were implemented using the python programming language. We tested the algorithm against the point in polygon algorithms used by the shapely (and by extension geopandas) library and the OpenCV library using points from the google Open Buildings project. Our algorithm in pure python performed much better than the shapely implementation. It also performed better than the OpenCV implementation when combined with the Numba optimization library. We also performed simulations to verify that our algorithm performance was of the order O(n).

cs.CG↗