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We prove an average-case depth hierarchy theorem for Boolean circuits over the standard basis of AND, OR, and NOT gates. Our hierarchy theorem says that for every d ≥ 2, there is an explicit n-variable Boolean function f, computed by a linear-size depth-d formula, which is such that any depth-(d -- 1) circuit that agrees with f on (1/2 + on(1)) fraction of all inputs must have size...
We study the complexity of approximating Boolean functions with DNFs and other depth-2 circuits, exploring two main directions: universal bounds on the approximability of all Boolean functions, and the approximability of the parity function. In the first direction, our main positive results are the first non-trivial universal upper bounds on approximability by DNFs: \begin{itemize} \item Every Boolean...
In this paper, we discuss how link stability and number of mobile nodes impact on end-to-end delay in mobile ad hoc network (MANET). We find that their relationship shows differently when there is a path between any arbitrary source-destination node pair in the network or not. Meanwhile, two models are proposed respectively based on the Cox proportional hazards model to reveal the relationship. It...
A three-dimensional thermo-mechanical coupled model of milling process has been developed using the rigid-viscoplastic finite element theory. Three-dimensional milling cutter model with spiral teeth and variational thickness cutting layer model are used in the new FEM model. Adaptive remeshing technique based on error estimate is adopted to control the computation scale and simulate the separation...
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