4. [HM45] One could provide an interpretation of the cognitive action that very much resembles the regularized risk in machine leaning. In this case, the kinetic energy can be regarded as the parsimony term, while the potentials are the penalties associated with the constraints.

However, in the cognitive action defined by the Lagrangian of Eq. (6.5.158), the potential comes with a flipped sign. If we use higher-order differential operators for defining the kinetic energy things might become different. Why?

#!# 5. [HM50] Provide conditions under which the day–night rhythmic conditions guarantee the satisfaction of w˙ (0) = w˙ (T ) = 0.