## 3 Results
### Simulated Data  
In order to assess performance on simulated data with known truth values, as is standard practice, we elected a simulated RNAseq count table data set with spiked values [24]. It has been created using a random number generator for the express purpose of benchmarking differential expression methodologies and consists of 10 samples, 5 \"cases\" and 5 \"controls\". Out of the 12,500 features, 1250 known features have spiked values.  
Our method highlights features in a manner different than usual statistical testing: instead of relying on statistical value thresh-holding, it trims the resulting lists according to the identification of pockets of organized and consistent behavior among the features investigated. Consequently, direct comparison to approaches such as t-testing can be difficult, especially on simulated data tailored to fit hypothesis testing. Simulated data sets created with random number generators exhibit none of the underlying biological constraints present in real data. Moreover, the differentially expressed features in biological systems tend to be organized in consistent networks.  
These differences lead us to expect that our method, which detects patterns of expression instead of statistical distributions, will underperform compared to hypothesis testing approaches in a simulated, spiked value data set. Even more importantly, our method aims to assess the information content of features' behavior across populations. Simulated data created using random number generators by definition exhibit highly stochastic behavior in the absence of biological constraints, which are difficult to model. Assessment of such a data set, in terms of information content should be expected to return few findings, if any, as there are no consistent patterns to be detected. Moreover, removal of the spiked values should reduce the findings even further, possibly eliminating them altogether.  
Indeed, entropic ranks underperformed in the identification of the spiked features as compared to limma on the simulated data, as can be seen in \"Supplementary Data 3--Output\". Testing the null hypothesis by removing the spiked values reduced performance even further, leading to the identification of 23 differentially expressed features by entropic ranks compared to a single differentially expressed feature returned by limma. However, investigation of these 23 differentially \"false positives\" showed that they represented rows for which the random number engine had failed to create properly uniform distributions across samples. Instead, these features were highly differentially expressed (15-fold or more) between populations, usually with a single outlying value in one of the two populations. Both under the null hypothesis and when using the full data, entropic ranks was more robust than rank products and \"entropic sums\" against false positive results. Its robustness was comparable with rank sums, which has convergence issues with high data dimensionality (see \"Supplementary Material 1--Method\", Part 5).  
This level of sensitivity to patterned behavior and robustness against false positive discoveries should be considered features of the method. Moreover, the plots created by entropic ranks during entropy calculation show very high entropy near the beginning of the distribution, and tend to oscillate around lower values further on. This pattern shows an initial low-entropy cluster behaving similar to the noise-dominated areas than we see in real data sets. Such behavior could help the experimenter identify poorly structured data sets.