15 research outputs found

    Approximate Profile Maximum Likelihood

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    We propose an efficient algorithm for approximate computation of the profile maximum likelihood (PML), a variant of maximum likelihood maximizing the probability of observing a sufficient statistic rather than the empirical sample. The PML has appealing theoretical properties, but is difficult to compute exactly. Inspired by observations gleaned from exactly solvable cases, we look for an approximate PML solution, which, intuitively, clumps comparably frequent symbols into one symbol. This amounts to lower-bounding a certain matrix permanent by summing over a subgroup of the symmetric group rather than the whole group during the computation. We extensively experiment with the approximate solution, and find the empirical performance of our approach is competitive and sometimes significantly better than state-of-the-art performance for various estimation problems

    Additional file 4: of Differential distribution and enrichment of non-coding RNAs in exosomes from normal and Cancer-associated fibroblasts in colorectal cancer

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    Figure S1. logFC-based MDS-plots (one for each type of lncRNA), where the first dimension corresponds to differences due to the type of sample (i.e. whether it is a normal cell, a tumor cell or an exosomal sample) and the second dimension corresponds to the differences between the samples themselves as biological replicates. The inferred dispersion and the Biological Coefficient of Variation (BCV) of all assayed samples for lncRNAs are 0.21201 and 0.4604, respectively, while the coefficients for sncRNA content are 0.25164 and 0.5016. These two coefficients reveal some interesting variation among samples. In this respect the multidimensional scaling (MDS) plots where the differences in ncRNA content between cellular and exosomal fractions and the heterogeneity of CAF samples, and especially their exosomes, are indicated as the main cause of this variation. Moreover, since each sequenced sample was prepared as a pool of three others and CAF samples and their exosomes are, as expected, more heterogenous because of their tumoral condition, then their variability should also be greater than that of NFs and their exosomes. Figure S1 also gives some differences that exist between NF and CAF exosomes. (PNG 104 kb

    Additional file 7: of Differential distribution and enrichment of non-coding RNAs in exosomes from normal and Cancer-associated fibroblasts in colorectal cancer

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    Mini web site presenting a dynamic venn diagram intersecting the relationships of significance from the assayed ncRNAs in the differential expression analyses performed between NF- and CAF- exosomes versus their respective cellular environments (i.e. NF-CELL versus NF-EXO and CAF-CELL versus CAF-EXO). Clicking on any intersected number, the web site opens a dialog summarizing the ncRNAs species that correspond to the intersection. (HTML 120 kb
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