Temporal order in living matters reflects the self-organizing nature of dynamical processes driven out thermodynamic equilibrium. Because functional reasons, period a biochemical oscillation must be tuned to specific value with precision; however, according uncertainty relation (TUR), precision oscillatory is constrained by cost generating it. After reviewing basics chemical oscillations using ...

We study local complexity measures for stochastic convex optimization problems, providing a minimax theory analogous to that of Hájek and Le Cam classical statistical problems. give complementary optimality results, developing fully online methods adaptively achieve optimal convergence guarantees. Our results provide function-specific lower bounds make precise correspondence between difficulty ...