A unified framework is proposed for dealing with matching rules of quasiperiodic patterns, relevant for both tiling models and real-world quasicrystals. The approach is intended for extraction and validation of a minimal set of matching rules, directly from the phased diffraction data. The construction yields precise values for the spatial density of distinct atomic positions and tolerates the presence of defects in a robust way.

中文翻译：

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准晶体的鲁棒最小匹配规则

提出了一个统一的框架来处理与平铺模型和现实世界准晶体相关的准周期模式的匹配规则。该方法旨在直接从相控衍射数据中提取和验证最小的匹配规则集。该结构可产生不同原子位置的空间密度的精确值，并以稳健的方式容忍缺陷的存在。