层次的威尔逊-考恩模型和连接矩阵
W A Zúñiga-Galindo1, B A Zambrano-Luna1
1School of Mathematical & Statistical Sciences, University of Texas Rio Grande Valley, One West University Blvd., Brownsville, TX 78520, USA.
Entropy (Basel, Switzerland)
|June 28, 2023
概括
这项研究引入了一种新的p-adic威尔逊-考恩模型,将神经连接矩阵集成为大脑动态. 这种新的框架克服了经典模型的局限性,使神经网络中小世界属性的分析成为可能.
科学领域:
- 计算神经科学是一种计算神经科学.
- 动态系统理论 动态系统理论
- 网络科学 网络科学
背景情况:
- 威尔逊 - 考恩模型描述了神经群体动态.
- 连接矩阵代表皮质神经线路.
- 经典模型很难结合复杂的网络结构,如小世界属性.
研究的目的:
- 调查威尔逊-考恩模型与连接矩阵之间的相互作用.
- 开发一种与经验神经连接数据相兼容的威尔逊-考万概括框架.
- 探索神经动力学的小世界属性.
主要方法:
- 在局部紧的阿贝尔群上制定威尔逊-考恩方程.
- 开发了威尔逊-考恩模型的p-adic版本.
- 使用神经网络模型和皮层连接矩阵的p-adic近似进行数值模拟.
主要成果:
- 在这些组上证明了考西问题对威尔逊-考万方程的正确性.
- 展示了经典的威尔逊-考恩模型与小世界属性不兼容.
- 根据经典预测和实验数据验证了p-adic威尔逊-考恩模型.
结论:
- 该p-adic威尔逊-考恩模型成功地结合了连接矩阵和神经网络属性.
- 这种通用模型为研究复杂的大脑网络动态提供了一条途径,包括小世界属性.
- 拟议的框架通过将动态模型与结构连接相结合,推进计算神经科学.
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