{'fraction_non_alphanumeric': 0.018387553041018388, 'fraction_numerical': 0.005657708628005658, 'mean_word_length': 4.7560975609756095, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
COMPUTING FIXED POINTS

This paper introduces theoretical measures of efficiency for triangulations used in computing fixed points. The measures, for both regular triangulations of R n and those with continuous refinement of grid size, are based on an average count of the number of simplices met by straight line segments. The computation of these measures is facilitated by a description of the facets as well as the vertices of a triangulation. We give a simple description of a modification of Eaves' and Saigal's K 3 and compute the measures of efficiency of three regular triangulations of R n and two triangulations of (0, 1] × R n with continuous refinement of grid size, including the modified K 3.