Balancing Straight-line Programs

We show that a context-free grammar of size that produces a single string of length (such a grammar is also called a string straight-line program) can be transformed in linear time into a context-free grammar for of size , whose unique derivation tree has depth . This solves an open problem in the area of grammar-based compression, improves many results in this area, and greatly simplifies many existing constructions. Similar results are shown for two formalisms for grammar-based tree compression: top dags and forest straight-line programs. These balancing results can be all deduced from a single meta-theorem stating that the depth of an algebraic circuit over an algebra with a certain finite base property can be reduced to with the cost of a constant multiplicative size increase. Here, refers to the size of the unfolding (or unravelling) of the circuit. In particular, this results applies to standard arithmetic circuits over (noncommutative) semirings.

Hybridization preceded radiation in diploid wheats

SummaryEvolutionary relationships among theAegilops-Triticumrelatives of cultivated wheats have been difficult to resolve owing to incomplete lineage sorting and reticulate evolution. Recent studies have suggested that the wheat D-genome lineage (progenitor ofAe. tauschii) originated through homoploid hybridization between the A-genome lineage (progenitor ofTriticums.str.) and the B-genome lineage (progenitor ofAe. speltoides). Scenarios of reticulation have been debated, calling for adequate phylogenetic analyses based on comprehensive sampling. To reconstruct the evolution ofAegilops-Triticumdiploids, we here combined high-throughput sequencing of 38 nuclear low-copy loci of multiple accessions of all 13 species with inferences of the species phylogeny using the full-parameterized MCMC_SEQ method. Phylogenies recovered a monophyleticAegilops-Triticumlineage that began diversifying ~6.5 Ma ago and gave rise to four sublineages, i.e. the A- (2 species), B- (1 species), D- (9 species) and T- (Ae. mutica) genome lineage. Full-parameterized phylogenies as well as patterns of tree dilation and tree compression supported a hybrid origin of the D-genome lineage from A and B ~4.1 Ma ago, and did not indicate additional hybridization events. This comprehensive and dated phylogeny of wheat relatives indicates that the origin of the hybrid D-genome was followed by intense diversification into almost all diploid as well as allopolyploid wild wheats.

Compressing Streams of Phylogenetic Trees

Bayesian Markov-Chain Monte Carlo (MCMC) methods for phylogenetic tree inference, that is, inference of the evolutionary history of distinct species using their molecular sequence data, typically generate large sets of phylogenetic trees. The trees generated by the MCMC procedure are samples of the posterior probability distribution that MCMC methods approximate. Thus, they generate a stream of correlated binary trees that need to be stored. Here, we adapt state-of-the art algorithms for binary tree compression to phylogenetic tree data streams and extend them to also store the required meta-data. On a phylogenetic tree stream containing 1, 000 trees with 500 leaves including branch length values, we achieve a compression rate of 5.4 compared to the uncompressed tree files and of 1.8 compared to bzip2-compressed tree files. For compressing the same trees, but without branch length values, our compression method is approximately an order of magnitude better than bzip2. A prototype implementation is available at https://github.com/axeltref/tree-compression.git.

Significance of lung anomalies in fetuses affected by tetralogy of Fallot with absent pulmonary valve syndrome

ObjectivesTetralogy of Fallot with absent pulmonary valve syndrome is a rare form of tetralogy of Fallot with dilatation of large pulmonary arteries. Prognosis is related to the severity of the cardiac malformation and to bronchial tree compression by dilated pulmonary arteries. This study analyses the prenatal echographic lung appearance in fetuses with tetralogy of Fallot with absent pulmonary valve and discusses its significance.MethodsWe carried out a retrospective review of fetal and postnatal files of nine fetuses diagnosed with tetralogy of Fallot with absent pulmonary valve syndrome in our institution. Correlations of prenatal ultrasound and cardiac imaging findings were obtained with outcome.ResultsAbnormal heterogeneous fetal lung echogenicity was detected in eight cases out of nine, always associated with significant lobar arterial dilatation. This aspect was well correlated with postnatal imaging and outcome in the four neonatal cases. The only fetus with normal lung echogenicity also had lower degree of pulmonary artery dilatation in the series.ConclusionsThis study demonstrates that a heterogeneous ultrasound appearance of the fetal lungs can be detected in utero in the most severe cases. This aspect suggests an already significant compression of the fetal bronchial tree by the dilated arteries that may have prognostic implications.