Single nucleotide variants (SNVs) have been discovered that they play crucial roles in disease pathogenesis as genetic factors. Featured by analyzing multiple SNVs in a biological module (e.g. exon, gene, etc.) collectively, the joint-SNVs studies are increasingly attractive in genome-wide association studies (GWASs), for which extensive efforts have been devoted to pursue effective multivariate methods. In this paper, we first reviewed several main streams of existing methods and their limitations in joint-SNVs studies. Then, we introduced a recently proposed novel method, namely statistic-space boundary based test (S-space BBT) to tackle these limitations. Via computational experiments on simulation datasets, not only we figured out the applicable scenarios for the six methods in considering the effect direction and whether the single significant is involved in, but also demonstrated the strong detecting sensitivity of S-space BBT under the different conditions of odds ratio, minor allele frequency, and the linkage disequilibrium. We anticipate that our study may provide clues for multivariate method selection, and that S-space BBT may play a promising role in the joint-SNVs analysis.

The analytic hierarchy process (AHP) is the most popular extension to the pairwise comparisons method which is based on the observation that it is much easier to rank several objects when restricted to two objects at one time. As the pairwise comparisons are subjective, the use of linguistic expres sions rather than numerical values is straightforward and friendlier due to the uncertainties that are inherent in human judgments. In this paper, to handle the uncertainty and hesitancy in practical decisionmaking situations, we represent pairwise comparisons in AHP using hesitant cloud linguistic term sets (HCLTSs) which are proposed based on hesitant fuzzy linguistic term sets (HFLTSs) and normal cloud models. Then, the synthetic cloud model aggregation algorithm is proposed to transform the HCLTS pairwise comparison matrix into the positive reciprocal synthetic cloud matrix. A prioritization method using the geometric mean technique is adopted, and the ranking method based on comparing of the parameters of normal cloud models is proposed. Thus, we extend the traditional AHP method in hesitant and uncertain environment, and we call it HCLTS-AHP method. The comparative linguistic expressions of preferences become more flexible and richer and are more similar to human beings’ cognitive models. Furthermore, the synthetic cloud model is consistent with objectivity and the calculations are easy to implement. An illustrated example is applied to the ranking of four alternatives to show the usefulness of the proposed HCLTS-AHP method.

Since Zadeh introduced fuzzy sets, a lot of extensions of this concept have been proposed, such as type-2 fuzzy sets, nonstationary fuzzy sets, and cloud models, to represent higher levels of uncertainty. This paper provides a comparative investigation of type-2 fuzzy sets, nonstationary fuzzy sets, and cloud models. Type-2 fuzzy sets study the fuzziness of the membership function (MF) using primary MF and secondary MF based on analytic mathematical methods; nonstationary fuzzy sets study the randomness of the MF using primary MF and variation function based on type-1 fuzzy sets theory; cloud models study the randomness of the distribution of samples in the universe and generate random membership grades (MGs) using two random variables based on probability and statistic mathematical methods. They all concentrate on dealing with the uncertainty of the MF or the MG which type-1 fuzzy sets do not consider, and thus have many similarities. Moreover, we find out that, the same qualitative concept “moderate amount” can be represented by an interval type-2 fuzzy set, a nonstationary fuzzy set or a normal cloud model, respectively. Then, we propose a unified mathematical expression for the interval type-2 fuzzy set, nonstationary fuzzy set and normal cloud model. On the other hand, we also find out that, the theory fundament and underlying motivations of these models are quite different. Therefore, We summarize detailed comparisons of distinctive properties of type-2 fuzzy sets, nonstationary fuzzy sets, and cloud models. Further, we study their diverse characteristics of distributions of MGs across vertical slices. The comparative investigation shows that these models are complementary to describe the uncertainty from different points of view. Thus, this paper provides a fundamental contribution and makes a basic reference for knowledge representation and other applications with uncertainty.

This paper proposes two viable computing strategies for distributed parallel systems: domain division with sub-domain overlapping and asynchronous communication. We have implemented a parallel computing procedure for simulation of Ti thin film growing process of a system with 1000 × 1000 atoms by means of the Monte Carlo (MC) method. This approach greatly reduces the computation time for simulation of large-scale thin film growth under realistic deposition rates. The multi-lattice MC model of deposition comprises two basic events: deposition, and surface diffusion. Since diffusion constitutes more than 90% of the total simulation time of the whole deposition process at high temperature, we concentrated on implementing a new parallel diffusion simulation that reduces communication time during simulation. Asynchronous communication and domain overlapping techniques are used to reduce the waiting time and communication time among parallel processors. The parallel algorithms we propose can simulate the thin film growth of a system with many more particles than before under realistic deposition rates, and can provide a more efficient means for computer simulation of thin film growth.