The astrocytes are cells which play an essential role in the functioning and interaction of neurons by feeding the respective neurons with calcium ions. Drawing inspiration from this two-way relationship in which the astrocytes influence and are influenced by the neurons by means of calcium ions, in this paper, we define and study spiking neural P systems with astrocytes producing calcium. Distinct from the usual firing rules in spiking neural P systems, the firing condition not only depends on the spikes collected in a neuron but also on the calcium units received from astrocytes. From the perspective of topological structure, the new variant is shown as a directed graph in which synapses link either astrocytes or neurons, as well as astrocytes to neurons and conversely. The computational power of spiking neural P systems with astrocytes producing calcium is investigated; it is proved that these systems using a limited number of rules are Turing universal as both number generating and number accepting devices. It is also presented how to obtain normal forms by removing forgetting rules and delays while preserving the computational power.

中文翻译：

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用产生钙的星形胶质细胞刺激神经 P 系统

星形胶质细胞是通过向各个神经元供给钙离子而在神经元的功能和相互作用中起重要作用的细胞。从星形胶质细胞通过钙离子影响和受神经元影响的这种双向关系中汲取灵感，在本文中，我们定义和研究了星形胶质细胞产生钙的尖峰神经 P 系统。与尖峰神经 P 系统中通常的放电规则不同，放电条件不仅取决于神经元中收集的尖峰，还取决于从星形胶质细胞接收的钙单元。从拓扑结构的角度来看，新变体显示为有向图，其中突触连接星形胶质细胞或神经元，以及星形胶质细胞与神经元，反之亦然。研究了用产生钙的星形胶质细胞刺激神经 P 系统的计算能力；事实证明，这些使用有限数量规则的系统是图灵通用的，既可以作为数字生成设备，也可以作为数字接受设备。还介绍了如何在保留计算能力的同时通过消除遗忘规则和延迟来获得范式。