Optimal skeleton huffman trees revisited

A skeleton Huffman tree is a Huffman tree in which all disjoint maximal perfect subtrees are shrunk into leaves. Skeleton Huffman trees, besides saving storage space, are also used for faster decoding and for speeding up Huffman-shaped wavelet trees. In 2017 Klein et al. introduced an optimal skeleton tree: for given symbol frequencies, it has the least number of nodes among all optimal prefix-free code trees (not necessarily Huffman’s) with shrunk perfect subtrees. Klein et al. described a simple algorithm that, for fixed codeword lengths, finds a skeleton tree with the least number of nodes; with this algorithm one can process each set of optimal codeword lengths to find an optimal skeleton tree. However, there are exponentially many such sets in the worst case. We describe an (formula presented)-time algorithm that, given n symbol frequencies, constructs an optimal skeleton tree and its corresponding optimal code. © Springer Nature Switzerland AG 2020.Supported by the Russian Science Foundation (RSF), project 18-71-00002

An improved diet for inland broodstock and the establishment of an inbred line from

Improved inland culturing methods for marine invertebrates are the most important prerequisite for the establishment of inbred lines. Here, we study the effects of improved diet on growth rates, survivorship and reproductive activities of the colonial urochordate Botryllus schlosseri, an important model species in a variety of scientific disciplines. Six long-term experiments (6−8 weeks each; 3−8 treatments per experiment) were conducted in an attempt to evaluate 10 different food types alone and in various combinations. We took a hierarchical approach in which some food types were contrasted and the results were used to design the next experimental set with new food types. A mixture of at least two types of diets was superior to any monotonous diet examined. Results were also characterized by high variability between colonies of the same hatch in any studied life history aspect, by the appearance of reproductive sterile colonies in the cultures, high survivorship, fast growing and long-lived colonies. The improved maintenance protocols enabled us to develop the first long-lived (> 6.5 years) inbred line of Botryllus with four successive generations of self-crossed pedigree animals

Allogeneic Responses between Three Remote Populations of the Cosmopolitan Ascidian Botryllus schlosseri(Immunology)

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