{'fraction_non_alphanumeric': 0.0070921985815602835, 'fraction_numerical': 0.0, 'mean_word_length': 5.830645161290323, '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}}
Discrete Spatial Filtering by Networks of Cells Facilitates Biological Pattern Formation

Interactions between neighboring cells are essential for generating or refining patterns in a number of biological systems. We propose a discrete filtering approach to predict how networks of cells modulate spatially varying input signals to produce more complicated or precise output signals. The interconnections between cells determine the set of spatial modes that are amplified or suppressed based on the coupling and internal dynamics of each cell, analogously to the way a traditional digital filter modifies the frequency components of a discrete signal. We apply our framework to two case studies in developmental biology, demonstrating that filtering analysis enhances our intuition regarding the behavior of interconnected multicellular systems.