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              <p>Cancer exhibits intra-tumor heterogeneity of gene expression that can be profiled using single-cell RNA sequencing technology. ‘Precision’ treatment strategies attempt to exploit this fortreatment recommendations tailored to patient-specific heterogeneity patterns in specific setsof genes (signatures). Identification of treatment-relevant signatures requires their observationacross multiple patients. However, inter-patient heterogeneity makes direct integration of geneexpression data across patients, and subsequent identification of signatures, unreliable.For the case of glioblastoma, Neftel et al. [1] have circumvented this problem using an ap-proach that first heuristically determines a candidate set of patient-specific signatures, and thenidentifies similar candidates across patients, to obtain biologically validated results.We expand and improve upon this approach using: (i) a statistically well-founded approachto score general signatures in individual patients, (ii) robust ranks instead of normalized RNAexpression levels, (iii) a straightforward extension of the patient-specific score to a global scoreacross all patients, and (iv) a gradient structure of the global score function.Since this binary partitioning problem is NP-complete, we use a randomized optimizationmethod in a multimodal setup, across 10,000 runs. Our greedy algorithm identifies signatures bystarting from a random gene set, then iteratively moves to the best signature in its neighborhood,using an efficient partial evaluation of the objective function, until a local optimum is found.Out of the seven 50-genes signatures that we found in the glioblastoma data set of 7,167genes and 6,855 cells, five had a high degree of similarity to all eight of the metaprogramsfrom the original study, with some of our signatures including genes from two metaprogramssimultaneously. Gene set enrichment analysis of one of the remaining two signatures identifieda specific neuronal process that is biologically plausible within the biological context.Our approach is free from ad-hoc thresholds, simple, transparent, robust, and can yieldbiologically plausible results. We believe that our approach allows for bypassing the need fora complicated process of generating individual signatures in every sample and their furtherintegration, and hence represents a useful addition to the tool belt of methods tackling thesignature search problem.</p>
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