{'fraction_non_alphanumeric': 0.017057569296375266, 'fraction_numerical': 0.0, 'mean_word_length': 5.266666666666667, '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}}
Nonlinear dynamics of large fluctuations

The distribution of paths for large fluctuations away from a stable state has been investigated, theoretically and by analog experiment. We have found critical broadening of the distribution of the paths coming to a cusp point representing the simplest generic singularity in the pattern of most probable (optimal) fluctuational paths in a non-equilibrium system. The critical behavior can be described by a Landau-type theory.