For each application a, we represent the mapping as a binary matrix ( beta _{a} in {0,1}^{|P_{a}| times |M|} ), with the elements β aij indicating whether application profile i of application a has been mapped to memory type j (β aij =1) or not (β aij =0).
By using the median (CR AIJ: 0.0683; CR AIP: 0.0674) or mean scenario (CR AIJ: 0.0745; CR AIP: 0.0587), the CRs were similar, but still much higher than the CR from AIJ by geometric mean, as expected.
Group-based approach adopts the techniques in AHP-group decision making called aggregation of individual judgments (AIJ) [42].
We prove a noncommutative version: for every matrixA= aij) such that supi Verbar;(aij)j‖l2and supj ‖ aij i‖l2are finite, there exists a matrix (bij) defining a bounded operator onl2, such that |aij|⩽|bij| for everyi, j.
The CR in the scenario of aggregation by geometric mean was markedly lower for AIJ than for AIP (CR AIJ: 0.0045; CR AIP: 0.0490), although only participants with a CR ≤ 0.1 were included for the AIP.
To address this need, a comprehensive comparison of wind loads and their effects on tall buildings is conducted utilizing eight major international codes/standards: ASCE 2010 (USA), AS/NZ 2011 (Australia and New Zealand), AIJ 2004 (Japan), CNS 2012 (China), NBCC 2010 (Canada), Eurocode 2010 (Europe), ISO 2009 and IWC 2012 (India).
The elements can take the values (aij, aji) = (1, 0), (0, 1), (1, 1), or (0, 0), and each value pair describes one of four types of genetic interactions between the signaling molecules Xi and Xj: (a) (0, 1) = Xi is upstream of Xj; (b) (1, 0) = Xi is downstream of Xj; (c) (0, 0) = Xi AND Xj; and (d) (1, 1) = Xi OR Xj (Figure 2B).
Table 3 Saaty semantic scale Aij Judgement 1 Equal important 3 W eak importance 5 Strong importance 7 Very strong importance 9 Absolute importance 2,4,6,8 Intermediate values.
If there is a link connecting nodes i and j, aij = 1; otherwise, 0. It is easy to verify that 4f(p) is equal to the mean squared edge lengths and 0≤f≤1.
The PSD of the alongwind generalized force of the fundamental mode is determined based on the Architectural Institute of Japan (AIJ) recommendations [7, 8].
where L = D - A is the graph Laplacian matrix for Gb, with D the diagonal degree matrix for A (i.e., Dii = ∑j Aij), and β1, β2 are nonnegative constants.
