## 4 Conclusions
### Features of Entropic Ranks  
In summary, the proposed method extends the rank product methodology by incorporating the measurement of information content as an integral part of the analysis and interpretation. Firstly, the selection of significant genes is based on the distribution of all genes over the entire populations, rather than evaluating each gene independently. Information-poor data, such as simulated data sets [24] with a very low signal-to-noise ratio exhibit a starkly different entropy distribution, without a defined, initial, low-entropy area followed by stably high entropy area with minimal oscillations (see \"Supplementary Material 2--Data Sets\" and \"Supplementary Material 3--Output\"). Secondly, the methodology is applicable to a broad array of selection problems and data types, as long as they conform to basic assumptions made by the rank products methodology. Thirdly, it departs from the adoption of arbitrary or empirical statistical thresholds, exploring the information density of the distribution and cherry picking clusters of high information content, through rigorous entropic analysis. Fourthly, the automation of the partition process is possible, allowing for unsupervised and unbiased analytical processes to be applied. The fifth feature is the ability to freely adjust the analytic granularity (by changing the sliding window step) to more refined or coarser inspection, enabling solutions of varying computational cost and level of convergence. Lastly, another advantage of this method is the potential for integration of data from different sources or dissection levels into the same analysis, as long as they can be transformed to similar, ranked value distributions.  
The following are available online at [[http://www.mdpi.com/2076-3417/10/20/7077/s1](http://www.mdpi.com/2076-3417/10/20/7077/s1)]([http://www.mdpi.com/2076-3417/10/20/7077/s1](http://www.mdpi.com/2076-3417/10/20/7077/s1)): \"Supplementary Material 1--Method.pdf\", \"Supplementary Material 2--Data Sets.pdf\", \"Supplementary Material 3--Output.Zr\". The following is available at [[http://doi.org/10.5281/zenodo.4028882](http://doi.org/10.5281/zenodo.4028882)]([http://doi.org/10.5281/zenodo.4028882](http://doi.org/10.5281/zenodo.4028882)): \"Supplementary Material 3--Output.Zr\".  
Conceptualization, A.C.; methodology, H.-X.d.L. and I.L.; software, H.-X.d.L.; validation, I.L. and H.-X.d.L.; writing--original draft preparation, H.-X.d.L. and I.L.; writing--review and editing, A.G.G., M.Z. and A.C.; supervision, A.C., A.G.G. and M.Z. All authors have read and agreed to the published version of the manuscript.  
**Funding:**: [PERSON]'s PhD thesis is supported by a scholarship from the State Scholarship Foundation in Greece (IKY) (Operational Program \"Human Resources Development--Education and Lifelong Learning\" Partnership Agreement (PA) 2014-2020). We acknowledge support of this work by the project \"ELIXIR-GR: Hellenic Research Infrastructure for the Management and Analysis of Data from the Biological Sciences\" (MIS 5002780) which is implemented under the action \"Reinforcement of the Research and Innovation Infrastructure\", funded by the Operational Program \"Competitiveness, Entrepreneurship and Innovation\" (NSRF 2014-2020) and co-financed by Greece and the European Union (European Regional Development Fund).  
**Acknowledgments:** [PERSON] is co-founder of e-NIOS PC.  
**Conflicts of Interest:** The authors declare no conflict of interest.