Vector space algebra for scaling and centering relationship matrices under non-Hardy–Weinberg equilibrium conditions

Background Scales are linear combinations of variables with coefficients that add up to zero and have a similar meaning to “contrast” in the analysis of variance. Scales are necessary in order to incorporate genomic information into relationship matrices for genomic selection. Statistical and biological parameterizations using scales under different assumptions have been proposed to construct alternative genomic relationship matrices. Except for the natural and orthogonal interactions approach (NOIA) method, current methods to construct relationship matrices assume Hardy–Weinberg equilibrium (HWE). The objective of this paper is to apply vector algebra to center and scale relationship matrices under non-HWE conditions, including orthogonalization by the Gram-Schmidt process. Theory and methods Vector space algebra provides an evaluation of current orthogonality between additive and dominance vectors of additive and dominance scales for each marker. Three alternative methods to center and scale additive and dominance relationship matrices based on the Gram-Schmidt process (GSP-A, GSP-D, and GSP-N) are proposed. GSP-A removes additive-dominance co-variation by first fitting the additive and then the dominance scales. GSP-D fits scales in the opposite order. We show that GSP-A is algebraically the same as the NOIA model. GSP-N orthonormalizes the additive and dominance scales that result from GSP-A. An example with genotype information on 32,645 single nucleotide polymorphisms from 903 Large-White × Landrace crossbred pigs is used to construct existing and newly proposed additive and dominance relationship matrices. Results An exact test for departures from HWE showed that a majority of loci were not in HWE in crossbred pigs. All methods, except the one that assumes HWE, performed well to attain an average of diagonal elements equal to one and an average of off diagonal elements equal to zero. Variance component estimation for a recorded quantitative phenotype showed that orthogonal methods (NOIA, GSP-A, GSP-N) can adjust for the additive-dominance co-variation when estimating the additive genetic variance, whereas GSP-D does it when estimating dominance components. However, different methods to orthogonalize relationship matrices resulted in different proportions of additive and dominance components of variance. Conclusions Vector space methodology can be applied to measure orthogonality between vectors of additive and dominance scales and to construct alternative orthogonal models such as GSP-A, GSP-D and an orthonormal model such as GSP-N. Under non-HWE conditions, GSP-A is algebraically the same as the previously developed NOIA model.

A Novel Multi-Objective Competitive Swarm Optimization Algorithm

In this article, a new algorithm, namely the multi-objective competitive swarm optimizer (MOCSO), is introduced to handle multi-objective problems. The algorithm has been principally motivated from the competitive swarm optimizer (CSO) and the NSGA-II algorithm. In MOCSO, a pair wise competitive scenario is presented to achieve the dominance relationship between two particles in the population. In each pair wise competition, the particle that dominates the other particle is considered the winner and the other is consigned as the loser. The loser particles learn from the respective winner particles in each individual competition. The inspired CSO algorithm does not use any memory to remember the global best or personal best particles, hence, MOCSO does not need any external archive to store elite particles. The experimental results and statistical tests confirm the superiority of MOCSO over several state-of-the-art multi-objective algorithms in solving benchmark problems.

An Adaptive Parallel PI-Skyline Query for Probabilistic and Incomplete Database

In the context of large quantities of information, the skyline query is a particularly useful tool for data mining and decision-making. However, the massive amounts of information on the Internet are frequently incomplete and uncertain due to data randomness, transmission errors, and many other reasons. Therefore, an efficient skyline query algorithm over an incomplete uncertain database is imperative. To address this issue, this paper proposes an efficient algorithm to apply skyline query on probabilistic incomplete data. The algorithm is based on U-Skyline model to avoid disadvantages of traditional P-Skyline model. The proposed methods introduce some novel concepts including transferred tuples, leading tuples and the new dominance relationship between probabilistic incomplete data. Besides, it is a parallel processing algorithm. Extensive experiments demonstrate the effectiveness and efficiency of the proposed algorithms.

Jaringan Sosial (Social Network) Antar Jantan Monyet Ekor Panjang (Macaca fascicularis) Di Gunung Meru, Padang, Sumatera Barat

A study on social network based on grooming interactions among males of long-tailed macaques (Macaca fascicularis) at Gunung Meru, Padang has been conducted from August to October 2015. The dominance relationship determined by submissive interactions among 17 adult males. Submissive interactions were recorded using ad libitum observation and grooming interactions by continuous recording method. The results showed that the dominance hierarchy among males was linear (Matman linearity index: h' = 0.97). Alfa male appeared to have the highest centrality index among all the males. This study indicates that individuals attained higher dominance hierarchy tend to have higher degree of centrality.