English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Neurons in the brain represent external stimuli via neural codes. These codesoften arise from stimulus-response maps, associating to each neuron a convexreceptive field. An important problem confronted by the brain is to inferproperties of a represented stimulus space without knowledge of the receptivefields, using only the intrinsic structure of the neural code. How does thebrain do this? To address this question, it is important to determine whatstimulus 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. Wefind that these objects can be expressed in a "canonical form" that directlytranslates to a minimal description of the receptive field structure intrinsicto the neural code. We consider the algebraic properties of homomorphismsbetween neural rings, which naturally relate to maps between neural codes. Weshow that maps between two neural codes are in bijection with ringhomomorphisms between the respective neural rings, and define the notion ofneural ring homomorphism, a special restricted class of ring homomorphismswhich preserve neuron structure. We also find connections to Stanley-Reisnerrings, and use ideas similar to those in the theory of monomial ideals toobtain an algorithm for computing the canonical form associated to any neuralcode, providing the groundwork for inferring stimulus space features fromneural activity alone.

The neural ring: using algebraic geometry to analyze neural codes