## 3 Results  
### Evaluation Criteria  
A threshold-free, adaptive, generalized selection process, like the one proposed, should be evaluated according to the following criteria: (a) specificity of the selected features in terms of biological relevance, (b) sensitivity to weak biological signals, (c) performance on data sets of varying noise content, and (d) its generality in terms of reliable performance across different types of experiments. To test against these criteria, we selected and analyzed a range of published, publicly accessible data sets, each tied to one or more of the aforementioned criteria. The chosen data sets (Table 2) and workflows used during analysis are presented more fully in \"Supplementary Material 2--Data Sets\". Biological relevance of the results was assessed with Gene Set Enrichment Analysis [20] tools EnrichR [21; 22] and BioInfoMiner [23]. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**GEO Accession** & **Organism** & **Type of Samples** & **Array** & **Samples** & **Cases** & **Controls** \\ \hline GSE12288 & H. sapiens & \begin{tabular}{c} Total RNA from \\ leukocytes in \\ peripheral blood \\ \end{tabular} & \begin{tabular}{c} Affymetrix Human \\ Genome U133A \\ Array \\ \end{tabular} & 222 & 110 & 112 \\ GSE69486 & H. sapiens & \begin{tabular}{c} Total RNA from \\ fibroblasts from skin \\ biopsies \\ \end{tabular} & \begin{tabular}{c} HumanHF-12 V4.0 \\ Expression Beadchip \\ \end{tabular} & 12 & 10 & 2 \\ GSE60767 & H. sapiens & \begin{tabular}{c} Total RNA was \\ extracted from \\ leukocytes \\ \end{tabular} & \begin{tabular}{c} Illumina \\ HumanHF-12 V3.0 \\ Expression Beadchip \\ \end{tabular} & 466 & 312 & 154 \\ GSE42861 & H. sapiens & \begin{tabular}{c} DNA from blood \\ leukocytes \\ \end{tabular} & \begin{tabular}{c} HumanHF-12 V4.0 \\ Expression Beadchip \\ \end{tabular} & 44 & 20 & 24 \\ SRP127667 & H. sapiens & \
\begin{tabular}{c} DNA from sorted \\ cardiac myocyte \\ nuclei \\ \end{tabular} &
\begin{tabular}{c} Illumina HiSeq 2500 \\ \end{tabular} & 13 & 10 & 3 \\ \hline \end{tabular}
\end{table} 
Table 2: GEO data sets used for verification. As an additional measure of verification, we compared its performance with the rank products and rank sums, both in their original form [4] and their recent implementation [7], as well as with the implementation of our entropic analysis upon the Rank Sum statistic (referred to as \"entropic sums\"). Moreover, SRP127667 was also tested for differential expression using EdgeR to verify the baseline biological relevance of results under a standard methodology since the application of rank statistics on RNAseq count data is novel. Overall, our approach exhibited consistent behavior on real as well as simulated data. Functional analysis of the derived feature lists showed that entropic ranks provides increased specificity at a concise list size, supporting the argument of efficient rejection of noise-dominated features. In short, entropic ranks lists produced highly relevant functional term lists in all cases, whereas other methodologies (rank products, \"entropic sums\", hypothesis testing, etc.) show variable performance according to experiment setup and thresh-holding values, ranging from comparable performance to lack of results. Discussion of the implementations and summaries of results is found in \"Supplementary Material 1--Method\". Discussion of the data sets and results of all methods applied on them are presented in \"Supplementary Material 2--Data Sets\". All files, tables and plots created are contained in \"Supplementary Material 3--Output\". This approach was adopted due to the fact that standard methodologies of comparison, such as list overlap, are inappropriate for two specific reasons. Firstly, they allow the assessment of interchangeability of two methods given similar thresh-holding choices, whereas entropic ranks were created to be a threshold-independent feature selection process.