作者
Carina Curto, Vladimir Itskov, Alan Veliz-Cuba, Nora Youngs
发表日期
2013/9
期刊
Bulletin of mathematical biology
卷号
75
页码范围
1571-1611
出版商
Springer US
简介
Neurons in the brain represent external stimuli via neural codes. These codes often arise from stereotyped stimulus-response maps, associating to each neuron a convex receptive field. An important problem confronted by the brain is to infer properties of a represented stimulus space without knowledge of the receptive fields, using only the intrinsic structure of the neural code. How does the brain do this? To address this question, it is important to determine what stimulus space features can—in principle—be extracted from neural codes. This motivates us to define the neural ring and a related neural ideal, algebraic objects that encode the full combinatorial data of a neural code. Our main finding is that these objects can be expressed in a “canonical form” that directly translates to a minimal description of the receptive field structure intrinsic to the code. We also find connections to Stanley–Reisner rings, and …
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C Curto, V Itskov, A Veliz-Cuba, N Youngs - Bulletin of mathematical biology, 2013