Avian embryos are a popular model for cell and developmental biologists. However, analysis of gene function in living embryos has been hampered by difficulties in targeting the expression of exogenous genes. We have developed a method for localized electroporation that overcomes some of the limitations of current techniques. We use a double-barreled suction electrode, backfilled with a solution containing a plasmid-encoding green fluorescent protein (GFP) and a neurophysiological stimulator to electroporate small populations of cells in living embryos. As many as 600 cells express GFP 24-48 h after electroporation. The number of cells that express GFP depends on the number of trains, the pulse frequency and the voltage. Surface epithelial cells and cells deep to the point of electroporation express GFP. No deformities result from electroporations, and neurons, neural crest, head mesenchyme, lens and otic placode cells have been transfected. This method overcomes some of the disadvantages of viral techniques, lipofection and in vivo electroporation. The method will be useful to biologists interested in tracing cell lineage or making genetic mosaic avian embryos.
Three standard subtree transfer operations for binary trees, used in particular for phylogenetic trees, are: tree bisection and reconnection (T BR), subtree prune and regraft (SP R) and rooted subtree prune and regraft (rSP R). For a pair of leaf-labelled binary trees with n leaves, the maximum number of such moves required to transform one into the other is n−Θ( √ n), extending a result of Ding, Grunewald and Humphries. We show that if the pair is chosen uniformly at random, then the expected number of moves required to transfer one into the other is n − Θ(n 2/3 ). These results may be phrased in terms of agreement forests: we also give extensions for more than two binary trees.
For a given number of colours, s, the guessing number of a graph is the base s logarithm of the size of the largest family of colourings of the vertex set of the graph such that the colour of each vertex can be determined from the colours of the vertices in its neighbourhood. An upper bound for the guessing number of the n-vertex cycle graph Cn is n/2. It is known that the guessing number equals n/2 whenever n is even or s is a perfect square [7]. We show that, for any given integer s ≥ 2, if a is the largest factor of s less than or equal to √ s, for sufficiently large odd n, the guessing number of Cn with s colours is (n − 1)/2 + log s (a). This answers a question posed by Christofides and Markström in 2011 [7]. We also present an explicit protocol which achieves this bound for every n. Linking this to index coding with side information, we deduce that the information defect of Cn with s colours is (n + 1)/2 − log s (a) for sufficiently large odd n. Our results are a generalisation of the s = 2 case which was proven in [3].
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