A common challenge in avian cell biology is the generation of differentiated cell-lines, especially in the keratinocyte lineage. Only a few avian cell-lines are available and very few of them show an interesting differentiation profile. During the last decade, mammalian embryonic stem cell-lines were shown to differentiate into almost all lineages, including keratinocytes. Although chicken embryonic stem cells had been obtained in the 1990s, few differentiation studies toward the ectodermal lineage were reported. Consequently, we explored the differentiation of chicken embryonic stem cells toward the keratinocyte lineage by using a combination of stromal induction, ascorbic acid, BMP4 and chicken serum. During the induction period, we observed a downregulation of pluripotency markers and an upregulation of epidermal markers. Three homogenous cell populations were derived, which were morphologically similar to chicken primary keratinocytes, displaying intracellular lipid droplets in almost every pavimentous cell. These cells could be serially passaged without alteration of their morphology and showed gene and protein expression profiles of epidermal markers similar to chicken primary keratinocytes. These cells represent an alternative to the isolation of chicken primary keratinocytes, being less cumbersome to handle and reducing the number of experimental animals used for the preparation of primary cells.

The topic of the article is the parametric study of the complexity of algorithms on arrays of pairwise distinct integers. We introduce a model that takes into account the non-uniformness of data, which we call the Ewens-like distribution of parameter θ for records on permutations: the weight θ r of a permutation depends on its number r of records. We show that this model is meaningful for the notion of presortedness, while still being mathematically tractable. Our results describe the expected value of several classical permutation statistics in this model, and give the expected running time of three algorithms: the Insertion Sort, and two variants of the Min-Max search.

TimSort is an intriguing sorting algorithm designed in 2002 for Python, whose worst-case complexity was announced, but not proved until our recent preprint. In fact, there are two slightly different versions of TimSort that are currently implemented in Python and in Java respectively. We propose a pedagogical and insightful proof that the Python version runs in time O(n log n). The approach we use in the analysis also applies to the Java version, although not without very involved technical details. As a byproduct of our study, we uncover a bug in the Java implementation that can cause the sorting method to fail during the execution. We also give a proof that Python's TimSort running time is in O(n + nH), where H is the entropy of the distribution of runs (i.e. maximal monotonic sequences), which is quite a natural parameter here and part of the explanation for the good behavior of TimSort on partially sorted inputs. Finally, we evaluate precisely the worst-case running time of Python's TimSort, and prove that it is equal to 1.5nH + O(n).

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