Rank aggregation is the process of aggregating multiple base rankers into a single but more comprehensive ranker, which plays an important role in many domains such as recommender system, meta-search, database, genomics, etc. Works related to the comparison of rank aggregation methods all don't have a suitable and general data generation mechanism to produce data with various characteristics and lack a more reasonable and effective algorithm evaluation performance index. Therefore, this paper presents a general data generation mechanism based on Mallows model to produce synthetic controllable datasets, uses generalized Kendall rank correlation coefficient and rank-biased overlap to evaluate and compare the performance of two kinds of methods under different settings. Besides, we also consider the comparison between indices and the impact of data characteristics on the algorithms. This paper may be helpful to researchers and decision-makers from multiple domains.

Gene expression is a fundamental process in a living system. The small RNAs (sRNAs) is widely observed as a global regulator in gene expression. The inherent nonlinearity in this regulatory process together with the bursty production of messenger RNA (mRNA), sRNA and protein make the exact solution for this stochastic process intractable. This is particularly the case when quantifying the protein noise level, which has great impact on multiple cellular processes. Here, we propose an approximate yet reasonably accurate solution for the gene expression noise with infrequent burst and strong regulation by sRNAs. This analytical solution allows us to better analyze the noise and stochastic deviation of protein level. We find that the regulation amplifies the noise, reduces the protein level. The stochasticity in the regulation generates more proteins than what if the stochasticity is removed from the system. The sRNA level is most important to the relationship between the noise and stochastic deviation. The results provide analytical tools for more general studies of gene expression and strengthen our quantitative understandings of post-transcriptional regulation in controlling gene expression processes.