作为光学模式的胚胎侧抑制：介观斑图形成的分析框架
Embryonic lateral inhibition as optical modes: an analytical framework for mesoscopic pattern formation
摘要：
在胚胎的许多发育阶段观察到细胞棋盘图案。我们研究了一个易于分析的侧抑制模型，并表明，耦合系数为负值是足够的，以获得嘈杂的或周期性的棋盘图案。我们解决的情况下，明确的线性链的细胞，并表明，嘈杂的反相关模式是在一个后临界制度$(ε_c < ε< 0)$。在亚临界状态$(-\infty < ε\leq ε_c)$中，周期性和交替的稳定状态是可用的，其中模式选择通过与声子的光学模式进行类比来确定。对于排列在六边形晶格中的细胞，亚临界模式可以被驱动成三种不同的状态：其中两种状态是周期性棋盘，第三种状态是两种周期性状态共存。
英文摘要：
Cellular checkerboard patterns are observed at many developmental stages of embryos. We study an analytically tractable model for lateral inhibition and show that a coupling coefficient with a negative value is sufficient to obtain noisy or periodic checkerboard patterns. We solve the case of a linear chain of cells explicitly and show that noisy anti-correlated patterns are available in a post-critical regime $(ε_c < ε< 0)$. In the sub-critical regime $(-\infty < ε\leq ε_c)$ a periodic and alternating steady state is available, where pattern selection is determined by making an analogy with the optical modes of phonons. For cells arranged in a hexagonal lattice, the sub-critical pattern can be driven into three different states: two of those states are periodic checkerboards and a third in which both periodic states coexist.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
