We consider the size of monotone circuits for quadratic boolean functions, that is, disjunctions of length-2 monomials. Our motivation is that a good (linear in the number of variables) lower bound on the monotone circuit size for a certain type of quadratic function would imply a good (even exponential) lower bound on the general non-monotone circuit size. To get more insight into the structur...

In this paper, new non-quadratic stability conditions are derived based on the parallel distributed compensation scheme to stabilize Takagi-Sugeno (T-S) fuzzy systems. We use a non-quadratic Lyapunov function as a fuzzy mixture of multiple quadratic Lyapunov functions. The quadratic Lyapunov functions share the same membership functions with the T-S fuzzy model. The stability conditions we prop...

High-dimensional longitudinal data arise frequently in biomedical and genomic research. It is important to select relevant covariates when the dimension of the parameters diverges as the sample size increases.We propose the penalized quadratic inference function to perform model selection and estimation simultaneously in the framework of a diverging number of regression parameters. The penalize...