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Abstract: As a newly introduced interconnection network for parallel computing, the locally twisted cube possesses many desirable properties. In this paper, mesh embeddings in locally twisted cubes are studied. Let LTQ n (V, E) denote the n-dimensional locally twisted cube. We present three major results in this paper: (1) For any integer n ⩾1, a 2×2 n−1 mesh can be embedded in LTQ n with dilation 1 and expansion 1. (2) For any integer n ⩾4, two node-disjoint 4×2 n−3 meshes can be embedded in LTQ n with dilation 1 and expansion 2. (3) For any integer n ⩾3, a 4 ×(2 n−2 −1) mesh can be embedded in LTQ n with dilation 2. The first two results are optimal in the sense that the dilations of all embeddings are 1. The embedding of the 2×2 n−1 mesh is also optimal in terms of expansion. We also present the analysis of 2p ×2q mesh embedding in locally twisted cubes. [Copyright &y& Elsevier]

Purpose – The purpose of this paper is to propose an economic cybernetics model based on the grey differential equation GM(1,N) for China's high-tech industries and provide the necessary support to assist high-tech industries management departments with their policy making. Design/methodology/approach – Based on the principle of grey differential equation GM(1,N), the grey differential equations of five high-tech industries in China are established using the net fixed assets, labor quantity and patent application quantity as cybernetics variables. After the discretization and first-order subtraction reduction to the simultaneous equation of the five grey models, a linear cybernetics model is resulted in. The structure parameters in the cybernetics system show explicit economic significance and can be identified through least square principle. At last, the actual data in 2004-2010 are introduced to empirically analyze the high-tech industrial system in China. Findings – The cybernetics system for China's high-tech industries are stable, observable, and controllable. On the whole, China's high-tech industries show higher output coefficients of the patent application quantity than those of net fixed assets and labor quantity. This suggests that China's industry development mainly depends on technological innovation rather than capital or labor inputs. It is expected that the total output value of China's high-tech industries will grow at an average annual rate of 15 percent in 2011-2015, with contributions of pharmaceuticals, aircraft and spacecraft, electronic and telecommunication equipments, computers and office equipments, medical equipments and meters by 21, 16, 13, 10, and 28 percent, respectively. In addition, pharmaceuticals, as well as medical equipments and meters, present upward proportions in the gross of Chinese high-tech industries significantly. Electronic and telecommunication equipments, plus computers and office equipments exhibit an obvious decreasing proportion. The proportion of the output value of aircraft and spacecraft is basically stable. Practical implications – Empirical analysis results are helpful for related management departments to formulate reasonable industrial policies to keep the sustained and stable development of the high-tech industries in China. Originality/value – Based on the grey differential equation GM(1,N), this research puts forward an economic cybernetics model for the high-tech industries in China. This model is applicable to the economic system with small sample data set. [ABSTRACT FROM AUTHOR]