Analysis of Combinatorial Neural Codes: An Algebraic Approach

A major problem in neuroscience is to understand how the brain uses neural activity to form representations of the external world. It is known that combinatorial information in the firing patterns of neurons often reflects important features of the stimuli which generated them. How can we efficiently extract such information? This chapter presents an algebraic method for encoding and extracting combinatorial structure from neural codes using the language of rings and ideals from commutative algebra. We also discuss how this structure can uncover principles of neural coding and infer topological features of the underlying stimulus space.