We present new algorithms for the solution of large structured Markov models whose in nitesimal generator can be expressed as a Kronecker expression of sparse matrices. We then compare them with the shu e-based method commonly used in this context and show how our new algorithms can be advantageous in dealing with very sparse matrices and in supporting both Jacobi-style and Gauss-Seidel-style methods with appropriate multiplication algorithms. Our main contribution is to show how solution algorithms based on Kronecker expression can be modi ed to consider probability vectors of size equal to the \actual" state space instead of the \potential" state space, thus providing space and time savings. The complexity of our algorithms is compared under di erent sparsity assumptions. A nontrivial example is studied to illustrate the complexity of the implemented algorithms.
Background. Gene fusions arising from chromosomal translocations have been implicated in cancer. RNA-seq has the potential to discover such rearrangements generating functional proteins (chimera/fusion). Recently, many methods for chimeras detection have been published. However, specificity and sensitivity of those tools were not extensively investigated in a comparative way. Results. We tested eight fusion-detection tools (FusionHunter, FusionMap, FusionFinder, MapSplice, deFuse, Bellerophontes, ChimeraScan, and TopHat-fusion) to detect fusion events using synthetic and real datasets encompassing chimeras. The comparison analysis run only on synthetic data could generate misleading results since we found no counterpart on real dataset. Furthermore, most tools report a very high number of false positive chimeras. In particular, the most sensitive tool, ChimeraScan, reports a large number of false positives that we were able to significantly reduce by devising and applying two filters to remove fusions not supported by fusion junction-spanning reads or encompassing large intronic regions. Conclusions. The discordant results obtained using synthetic and real datasets suggest that synthetic datasets encompassing fusion events may not fully catch the complexity of RNA-seq experiment. Moreover, fusion detection tools are still limited in sensitivity or specificity; thus, there is space for further improvement in the fusion-finder algorithms.
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