Negative entanglement measure for bipartite separable mixed states

We define a negative entanglement measure for separable states which shows that how much entanglement one should compensate the unentangled state at least for changing it into an entangled state. For two-qubit systems and some special classes of states in higher-dimensional systems, the explicit formula and the lower bounds for the negative entanglement measure have been presented, and it always vanishes for bipartite separable pure states. The negative entanglement measure can be used as a useful quantity to describe the entanglement dynamics and the quantum phase transition. In the transverse Ising model, the first derivatives of negative entanglement measure diverge on approaching the critical value of the quantum phase transition, although these two-site reduced density matrices have no entanglement at all. In the 1D Bose-Hubbard model, the NEM as a function of $t/U$ changes from zero to negative on approaching the critical point of quantum phase transition.Comment: 6 pages, 3 figure

Patterns and influencing factor of synonymous codon usage in porcine circovirus

<p>Abstract</p> <p>Background</p> <p>Analysis of codon usage can reveal much about the molecular evolution of the viruses. Nevertheless, little information about synonymous codon usage pattern of porcine circovirus (PCV) genome in the process of its evolution is available. In this study, to give a new understanding on the evolutionary characteristics of PCV and the effects of natural selection from its host on the codon usage pattern of the virus, Patterns and the key determinants of codon usage in PCV were examined.</p> <p>Methods</p> <p>We carried out comprehensive analysis on codon usage pattern in the PCV genome, by calculating relative synonymous codon usage (RSCU), effective number of codons (ENC), dinucleotides and nucleic acid content of the PCV genome.</p> <p>Results</p> <p>PCV genomes have relatively much lower content of GC and codon preference, this result shows that nucleotide constraints have a major impact on its synonymous codon usage. The results of the correspondence analysis indicate codon usage patterns of PCV of various genotypes, various subgenotypes changed greatly, and significant differences in codon usage patterns of Each virus of Circoviridae.There is much comparability between PCV and its host in their synonymous codon usage, suggesting that the natural selection pressure from the host factor also affect the codon usage patterns of PCV. In particular, PCV genotype II is in synonymous codon usage more similar to pig than to PCV genotype I, which may be one of the most important molecular mechanisms of PCV genotype II to cause disease. The calculations results of the relative abundance of dinucleotides indicate that the composition of dinucleotides also plays a key role in the variation found in synonymous codon usage in PCV. Furthermore, geographic factors, the general average hydrophobicity and the aromaticity may be related to the formation of codon usage patterns of PCV.</p> <p>Conclusion</p> <p>The results of these studies suggest that synonymous codon usage pattern of PCV genome are the result of interaction between mutation pressure and natural selection from its host. The information from this study may not only have theoretical value in understanding the characteristics of synonymous codon usage in PCV genomes, but also have significant value for the molecular evolution of PCV.</p