Topologies and Laplacian spectra of a deterministic uniform recursive tree

The uniform recursive tree (URT) is one of the most important models and has been successfully applied to many fields. Here we study exactly the topological characteristics and spectral properties of the Laplacian matrix of a deterministic uniform recursive tree, which is a deterministic version of URT. Firstly, from the perspective of complex networks, we determine the main structural characteristics of the deterministic tree. The obtained vigorous results show that the network has an exponential degree distribution, small average path length, power-law distribution of node betweenness, and positive degree-degree correlations. Then we determine the complete Laplacian spectra (eigenvalues) and their corresponding eigenvectors of the considered graph. Interestingly, all the Laplacian eigenvalues are distinct.Comment: 7 pages, 1 figures, definitive version accepted for publication in EPJ

Caenorhabditis briggsae Recombinant Inbred Line Genotypes Reveal Inter-Strain Incompatibility and the Evolution of Recombination

The nematode Caenorhabditis briggsae is an emerging model organism that allows evolutionary comparisons with C. elegans and exploration of its own unique biological attributes. To produce a high-resolution C. briggsae recombination map, recombinant inbred lines were generated from reciprocal crosses between two strains and genotyped at over 1,000 loci. A second set of recombinant inbred lines involving a third strain was also genotyped at lower resolution. The resulting recombination maps exhibit discrete domains of high and low recombination, as in C. elegans, indicating these are a general feature of Caenorhabditis species. The proportion of a chromosome's physical size occupied by the central, low-recombination domain is highly correlated between species. However, the C. briggsae intra-species comparison reveals striking variation in the distribution of recombination between domains. Hybrid lines made with the more divergent pair of strains also exhibit pervasive marker transmission ratio distortion, evidence of selection acting on hybrid genotypes. The strongest effect, on chromosome III, is explained by a developmental delay phenotype exhibited by some hybrid F2 animals. In addition, on chromosomes IV and V, cross direction-specific biases towards one parental genotype suggest the existence of cytonuclear epistatic interactions. These interactions are discussed in relation to surprising mitochondrial genome polymorphism in C. briggsae, evidence that the two strains diverged in allopatry, the potential for local adaptation, and the evolution of Dobzhansky-Muller incompatibilities. The genetic and genomic resources resulting from this work will support future efforts to understand inter-strain divergence as well as facilitate studies of gene function, natural variation, and the evolution of recombination in Caenorhabditis nematodes

Magnetic Losses up to Saturation in Non-Oriented Steel Lamination

The efficiency of electrical machines has global impact and its improvement passes through a good knowledge of the magnetic cores properties, namely the energy loss. One difficult aspect of the loss investigation in magnetic sheets concerns the appraisal of the material behavior at polarizations close to the saturation value Js, where most efficient rotating machines are made to work. In this communication such a behavior is experimentally assessed exploiting a novel magnetizing system, where non-oriented Fe-Si steel sheets can be characterized under alternating and rotational flux in the frequency range 2 Hz – 1 kHz up to the polarization value Jp≅0.98 Js