{'fraction_non_alphanumeric': 0.022511848341232227, 'fraction_numerical': 0.0, 'mean_word_length': 5.926229508196721, '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}}
Analytic solution of stochastic completion fields

Uses generalized particle trajectories to derive an analytic expression characterizing the probability distribution of boundary-completion shape. This is essential to the understanding of the perceptual phenomenon of illusory (subjective) contours. The particles' dynamics include Poisson-distributed ensembles of driving forces as well as particle decay. The resulting field, representing completed surface boundaries, is characterized by the fraction of particles at x with velocity x/spl dot/. The distributions are projectively covariant in the sense that fields calculated in any lower-dimensional projection correspond to the projections of fields calculated in any higher dimension. Being analytic, the relationship between velocity, diffusivity, and decay can be made readily apparent.