A study on the relations between the topological parameter and entanglement

In this paper, some relations between the topological parameter $d$ and concurrences of the projective entangled states have been presented. It is shown that for the case with $d=n$, all the projective entangled states of two $n$-dimensional quantum systems are the maximally entangled states (i.e. $C=1$). And for another case with $d\neq n$, $C$ both approach $0$ when $d\rightarrow +\infty$ for $n=2$ and $3$. Then we study the thermal entanglement and the entanglement sudden death (ESD) for a kind of Yang-Baxter Hamiltonian. It is found that the parameter $d$ not only influences the critical temperature $T_{c}$, but also can influence the maximum entanglement value at which the system can arrive at. And we also find that the parameter $d$ has a great influence on the ESD.Comment: 8 pages, 5 figure

Method of constructing braid group representation and entanglement in a Yang-Baxter sysytem

In this paper we present reducible representation of the $n^{2}$ braid group representation which is constructed on the tensor product of n-dimensional spaces. By some combining methods we can construct more arbitrary $n^{2}$ dimensional braiding matrix S which satisfy the braid relations, and we get some useful braiding matrix S. By Yang-Baxteraition approach, we derive a $9\times9$ unitary $\breve{R}$ according to a $9\times9$ braiding S-matrix we have constructed. The entanglement properties of $\breve{R}$-matrix is investigated, and the arbitrary degree of entanglement for two-qutrit entangled states can be generated via $\breve{R}(\theta, \phi_{1},\phi_{2})$-matrix acting on the standard basis.Comment: 9 page

Fractionation statistics

<p>Abstract</p> <p>Background</p> <p>Paralog reduction, the loss of duplicate genes after whole genome duplication (WGD) is a pervasive process. Whether this loss proceeds gene by gene or through deletion of multi-gene DNA segments is controversial, as is the question of fractionation bias, namely whether one homeologous chromosome is more vulnerable to gene deletion than the other.</p> <p>Results</p> <p>As a null hypothesis, we first assume deletion events, on one homeolog only, excise a geometrically distributed number of genes with unknown mean <it>µ</it>, and these events combine to produce deleted runs of length l, distributed approximately as a negative binomial with unknown parameter <it>r</it>, itself a random variable with distribution <it>π</it>(·). A more realistic model requires deletion events on both homeologs distributed as a truncated geometric. We simulate the distribution of run lengths <it>l</it> in both models, as well as the underlying <it>π</it>(<it>r</it>), as a function of <it>µ</it>, and show how sampling <it>l</it> allows us to estimate <it>µ</it>. We apply this to data on a total of 15 genomes descended from 6 distinct WGD events and show how to correct the bias towards shorter runs caused by genome rearrangements. Because of the difficulty in deriving <it>π</it>(·) analytically, we develop a deterministic recurrence to calculate each <it>π</it>(<it>r</it>) as a function of <it>µ</it> and the proportion of unreduced paralog pairs.</p> <p>Conclusions</p> <p>The parameter <it>µ</it> can be estimated based on run lengths of single-copy regions. Estimates of <it>µ</it> in real data do not exclude the possibility that duplicate gene deletion is largely gene by gene, although it may sometimes involve longer segments.</p

Sufficient conditions for super k-restricted edge connectivity in graphs of diameter 2

AbstractFor a connected graph G=(V,E), an edge set S⊆E is a k-restricted edge cut if G−S is disconnected and every component of G−S has at least k vertices. The k-restricted edge connectivity of G, denoted by λk(G), is defined as the cardinality of a minimum k-restricted edge cut. Let ξk(G)=min{|[X,X¯]|:|X|=k,G[X]is connected}. G is λk-optimal if λk(G)=ξk(G). Moreover, G is super-λk if every minimum k-restricted edge cut of G isolates one connected subgraph of order k. In this paper, we prove that if |NG(u)∩NG(v)|≥2k−1 for all pairs u, v of nonadjacent vertices, then G is λk-optimal; and if |NG(u)∩NG(v)|≥2k for all pairs u, v of nonadjacent vertices, then G is either super-λk or in a special class of graphs. In addition, for k-isoperimetric edge connectivity, which is closely related with the concept of k-restricted edge connectivity, we show similar results