The problem of testing monotonicity of a Boolean function f : {0, 1}n → {0, 1} has received much attention recently. Denoting the proximity parameter by ε, the best tester is the non-adaptive Õ( √ n/ε) tester of Khot-Minzer-Safra (FOCS 2015). Let I(f) denote the total influence of f . We give an adaptive tester whose running time is I(f)poly(ε logn).

We show that there do not exist adaptive confidence bands for curve estimation except under very restrictive assumptions. We propose instead to construct adaptive bands that cover a surrogate function f which is close to, but simpler than, f . The surrogate captures the significant features in f . We establish lower bounds on the width for any confidence band for f and construct a procedure tha...

This study investigates how students’ prior expectations of technology affect overall learning outcomes across two adaptive systems, one gamebased (iSTART-ME) and one non-game based (iSTART-Regular). The current study (n=83) is part of a larger study (n=124) intended to teach reading comprehension strategies to high school students. Results revealed that students’ prior expectations impacted le...

in this paper, the problem of decentralized model reference adaptive control (mrac) for a class of large scale systems with time varying delay in interconnected term and input and state delays is studied. to compensate the effect of input delay indirectly, a smith predictor built on. to handle the effects of the time delays in input, the adaptive controller part includes two auxiliary dynamic f...

|We study minimax-rate adaptive estimation for density classes indexed by continuous hyper-parameters. The classes are assumed to be partially ordered in terms of inclusion relationship. Under a mild condition on the minimax risks, we show that a minimax-rate adaptive estimator can be constructed for the classes. 1 Problem of interest This paper concerns adaptive density estimation. Information...