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The Analytic Hierarchy Process (AHP) is a much discussed method in ranking business alternatives based on empirical and judgemental information. We focus here upon the key component of deducing efficient vectors for a reciprocal matrix of pair-wise comparisons. It has been shown that the entry-wise geometric mean of all columns is efficient for any reciprocal matrix. Here, by combining some new basic observations with some known theory, we (1) give a method for inductively generating large collections of efficient vectors, and (2) show that the entry-wise geometric mean of any collection of distinct columns of a reciprocal matrix is efficient. We study numerically, using different measures, the performance of these geometric means in approximating the reciprocal matrix by a consistent matrix. We conclude that, as a general method to be chosen, independent of the data, the geometric mean of all columns performs well when compared with the geometric mean of proper subsets of columns.

 

The phagocytosis and destruction of pathogens in lysosomes constitute central elements of innate immune defense. Here, we show that Brucella , the causative agent of brucellosis, the most prevalent bacterial zoonosis globally, subverts this immune defense pathway by activating regulated IRE1α-dependent decay (RIDD) of Bloc1s1 mRNA encoding BLOS1, a protein that promotes endosome–lysosome fusion. RIDD-deficient cells and mice harboring a RIDD-incompetent variant of IRE1α were resistant to infection. Inactivation of the Bloc1s1 gene impaired the ability to assemble BLOC-1-related complex (BORC), resulting in differential recruitment of BORC-related lysosome trafficking components, perinuclear trafficking of Brucella -containing vacuoles (BCVs), and enhanced susceptibility to infection. The RIDD-resistant Bloc1s1 variant maintains the integrity of BORC and a higher-level association of BORC-related components that promote centrifugal lysosome trafficking, resulting in enhanced BCV peripheral trafficking and lysosomal destruction, and resistance to infection. These findings demonstrate that host RIDD activity on BLOS1 regulates Brucella intracellular parasitism by disrupting BORC-directed lysosomal trafficking. Notably, coronavirus murine hepatitis virus also subverted the RIDD–BLOS1 axis to promote intracellular replication. Our work establishes BLOS1 as a novel immune defense factor whose activity is hijacked by diverse pathogens.