{'fraction_non_alphanumeric': 0.04071661237785016, 'fraction_numerical': 0.04560260586319218, 'mean_word_length': 5.684782608695652, '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}}
A functorial approach to the behaviour of multidimensional control systems

It is well known that the controllability of a linear multidimensional control system depends on an algebraic property (namely, the torsion-freeness) of a certain module M associated with the system (Oberst, 1990; Pillai and Shankar, 1999; Pommaret and Quadrat, 1999a; 1999b). The recent survey (Wood, 2000) gives different equivalent formulations of controllability and, in particular, the equivalence obtained in (Pillai and Shankar, 1999) between the torsion-freeness of M and the definition of controllability given by Willems (1991).