Fixed-to-Variable Length Distribution Matching

Fixed-to-variable length (f2v) matchers are used to reversibly transform an input sequence of independent and uniformly distributed bits into an output sequence of bits that are (approximately) independent and distributed according to a target distribution. The degree of approximation is measured by the informational divergence between the output distribution and the target distribution. An algorithm is developed that efficiently finds optimal f2v codes. It is shown that by encoding the input bits blockwise, the informational divergence per bit approaches zero as the block length approaches infinity. A relation to data compression by Tunstall coding is established.Comment: 5 pages, essentially the ISIT 2013 versio

A new balance index for phylogenetic trees

Several indices that measure the degree of balance of a rooted phylogenetic tree have been proposed so far in the literature. In this work we define and study a new index of this kind, which we call the total cophenetic index: the sum, over all pairs of different leaves, of the depth of their least common ancestor. This index makes sense for arbitrary trees, can be computed in linear time and it has a larger range of values and a greater resolution power than other indices like Colless' or Sackin's. We compute its maximum and minimum values for arbitrary and binary trees, as well as exact formulas for its expected value for binary trees under the Yule and the uniform models of evolution. As a byproduct of this study, we obtain an exact formula for the expected value of the Sackin index under the uniform model, a result that seems to be new in the literature.Comment: 24 pages, 2 figures, preliminary version presented at the JBI 201

Destruction of very simple trees

We consider the total cost of cutting down a random rooted tree chosen from a family of so-called very simple trees (which include ordered trees, $d$-ary trees, and Cayley trees); these form a subfamily of simply generated trees. At each stage of the process an edge is chose at random from the tree and cut, separating the tree into two components. In the one-sided variant of the process the component not containing the root is discarded, whereas in the two-sided variant both components are kept. The process ends when no edges remain for cutting. The cost of cutting an edge from a tree of size $n$ is assumed to be $n^\alpha$. Using singularity analysis and the method of moments, we derive the limiting distribution of the total cost accrued in both variants of this process. A salient feature of the limiting distributions obtained (after normalizing in a family-specific manner) is that they only depend on $\alpha$.Comment: 20 pages; Version 2 corrects some minor error and fixes a few typo

Mycosphaerella podagrariae - a necrotrophic phytopathogen forming a special cellular interaction with its host Aegopodium podagraria

We present a new kind of cellular interaction found between Mycosphaerella podagrariae and Aegopodium podagraria, which is remarkably different to the interaction type of the obligate biotrophic fungus Cymadothea trifolii, another member of the Mycosphaerellaceae (Capnodiales, Dothideomycetes, Ascomycota) which we have described earlier. Observations are based on both conventional and cryofixed material and show that some features of this particular interaction are better discernable after chemical fixation. We were also able to generate sequences for nuclear ribosomal DNA (complete SSU, 5.8 S and flanking ITS-regions, D1–D3 region of the LSU) confirming the position of M. podagrariae within Mycosphaerellacea