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Full-Text Articles in Algebraic Geometry
The Neural Ring: Using Algebraic Geometry To Analyze Neural Codes, Nora Youngs
The Neural Ring: Using Algebraic Geometry To Analyze Neural Codes, Nora Youngs
Department of Mathematics: Dissertations, Theses, and Student Research
Neurons in the brain represent external stimuli via neural codes. These codes often arise from 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 …