Permutation tests are widely used in statistics, providing a finite-sample guarantee on the type I error rate whenever distribution of samples under null hypothesis is invariant to some rearrangement. Despite its increasing popularity and empirical success, theoretical properties permutation test, especially power, have not been fully explored beyond simple cases. In this paper, we attempt part...

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 ...