For testing both one-sided and two-sided hypotheses concerning several treatment arms in group sequentially performed clinical trials with arbitrary outcome variables, a general method is considered that allows one to completely self-design a study. All information available prior to a stage is used for estimating the sample size and the weight for the next step. In "using up" the variance, the...

Existing depth separation results for constant-depth networks essentially show that certain radial functions in $$\mathbb {R}^d$$ , which can be easily approximated with 3 networks, cannot by 2 even up to constant accuracy, unless their size is exponential d. However, the used demonstrate this are rapidly oscillating, a Lipschitz parameter scaling polynomially dimension d (or equivalently, func...

This paper presents a new family of complex spreading sequences designed using mutually orthogonal(MO) complementary sets. Based on the technique described in this paper, the correlation properties ofsets ofsequences are compared to well-known Walsh-Hadamard sequence sets. Further improvement of correlation qualities can be achieved by employing a diagonal modification method. We also present s...