Sparse neural codes and convexity
Sparse neural codes and convexity
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稀疏神经代码和凸性
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Nora Youngs
中科院分区：
文献类型：
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作者：
R. A. Jeffs;Mohamed Omar;Natchanon Suaysom;A. Wachtel;Nora Youngs
确定大脑如何存储信息是神经科学中最紧迫的问题之一。在许多情况下，给定神经元的刺激集合可以通过$\mathbb{R}^d$中的凸集来建模。然后，可以使用被称为神经代码的组合对象来提取这些凸区域所覆盖的空间的特征。我们应用凸几何的结果来确定哪些神经代码可以通过开凸集的排列来实现。我们限制我们的注意力主要是在低维稀疏码。我们发现，相交完备性特征的可实现的2 $-稀疏码，并表明，任何可实现的2 $-稀疏码的嵌入维数最多为3 $。此外，我们还证明了在$\mathbb{R}^2$和$\mathbb{R}^3$中，2 $-稀疏码的闭集实现与开集实现是等价的，从而为区分哪些2 $-稀疏码的嵌入维数不超过2 $提供了一些初步的结果.
Determining how the brain stores information is one of the most pressing problems in neuroscience. In many instances, the collection of stimuli for a given neuron can be modeled by a convex set in $\mathbb{R}^d$. Combinatorial objects known as \emph{neural codes} can then be used to extract features of the space covered by these convex regions. We apply results from convex geometry to determine which neural codes can be realized by arrangements of open convex sets. We restrict our attention primarily to sparse codes in low dimensions. We find that intersection-completeness characterizes realizable $2$-sparse codes, and show that any realizable $2$-sparse code has embedding dimension at most $3$. Furthermore, we prove that in $\mathbb{R}^2$ and $\mathbb{R}^3$, realizations of $2$-sparse codes using closed sets are equivalent to those with open sets, and this allows us to provide some preliminary results on distinguishing which $2$-sparse codes have embedding dimension at most $2$.