Polarization of neural codes
Polarization of neural codes
复制标题
神经编码的极化
DOI：
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发表时间：
2018
影响因子：
1
通讯作者：
H. Kulosman
中科院分区：
文献类型：
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作者：
Katie Christensen;H. Kulosman
神经环和神经理想作为分析神经码内在结构的代数工具是由C.~ Curto et al.，2013年。从那时起，他们在几篇论文中进行了研究，包括G“unt“urk“un等人2017年的论文，其中引入了神经理想极化的概念。在本文中，我们扩展了他们的想法，通过引入极化的图案和神经代码的概念。我们表明，我们介绍的概念有非常好的属性，可以让学习的内在结构的神经代码的长度$n$通过平方自由单项式理想在$2n$变量和解释的结果回到原来的神经代码的环境空间。
在本文的最后一节中，我们介绍了不活跃的神经元，部分神经代码和部分图案的概念，以及这些代码和图案的极化的概念。我们使用这些概念给一个定理的一个新的证明文件G“unt“urk“un等。
The neural rings and ideals as an algebraic tool for analyzing the intrinsic structure of neural codes were introduced by C.~Curto et al. in 2013. Since then they were investigated in several papers, including the 2017 paper by G"unt"urk"un et al., in which the notion of polarization of neural ideals was introduced. In this paper we extend their ideas by introducing the notions of polarization of motifs and neural codes. We show that the notions that we introduced have very nice properties which could allow the studying of the intrinsic structure of neural codes of length $n$ via the square free monomial ideals in $2n$ variables and interpreting the results back in the original neural code ambient space.
In the last section of the paper we introduce the notions of inactive neurons, partial neural codes, and partial motifs, as well as the notions of polarization of these codes and motifs. We use these notions to give a new proof of a theorem from the paper by G"unt"urk"un et al. that we mentioned above.