Neural and perceptual manifolds regarded geometrically

Challenges face the neuroscientist when probing an organism's nervous system yields hundreds or thousands of simultaneous independently recorded signals. One way of dealing with this is to gather all n signals into a single point in an n-dimensional space, called the state of the nervous system. Structures created by the assembly of states formed by a coherent behavioral entity, such as the generalized sensing or perceiving of an object or the performing of a motor action, are called manifolds. Geometrical operations involving manifold properties have the potential of characterizing the neural organization underlying observed modules of behavior and predicting expected changes with learning or with the passage along streams of neural processing. Manifold analysis depends critically on the nature of the entered data and the match of the mathematical and computational tools applied to them.