Theory of DNA translocation through narrow ion channels and nanopores with charged walls

Translocation of a single stranded DNA through genetically engineered $\alpha$-hemolysin channels with positively charged walls is studied. It is predicted that transport properties of such channels are dramatically different from neutral wild type $\alpha$-hemolysin channel. We assume that the wall charges compensate the fraction $x$ of the bare charge $q_{b}$ of the DNA piece residing in the channel. Our prediction are as follows (i) At small concentration of salt the blocked ion current decreases with $x$. (ii) The effective charge $q$ of DNA piece, which is very small at $x = 0$ (neutral channel) grows with $x$ and at $x=1$ reaches $q_{b}$. (iii) The rate of DNA capture by the channel exponentially grows with $x$. Our theory is also applicable to translocation of a double stranded DNA in narrow solid state nanopores with positively charged walls.Comment: 3 pages, 1 figur

A quantum model for the magnetic multi-valued recording

We have proposed a quantum model for the magnetic multi-valued recording in this paper. The hysteresis loops of the two-dimensional systems with randomly distributed magnetic atoms have been studied by the quantum theory developed previously. The method has been proved to be exact in this case. We find that the single-ion anisotropies and the densities of the magnetic atoms are mainly responsible for the hysterisis loops. Only if the magnetic atoms contained by the systems are of different (not uniform) anistropies and their density is low, there may be more sharp steps in the hysteresis loops. Such materials can be used as the recording media for the so-called magnetic multi-valued recording. Our result explained the experimental results qualitativly.Comment: 10 pages containing one Table. Latex formatted. 5 figures: those who are interested please contact the authors requiring the figures. Submitted to J. Magn. Magn. Mater. . Email address: [email protected]

The Algorithmic Complexity of Bondage and Reinforcement Problems in bipartite graphs

Let $G=(V,E)$ be a graph. A subset $D\subseteq V$ is a dominating set if every vertex not in $D$ is adjacent to a vertex in $D$. The domination number of $G$, denoted by $\gamma(G)$, is the smallest cardinality of a dominating set of $G$. The bondage number of a nonempty graph $G$ is the smallest number of edges whose removal from $G$ results in a graph with domination number larger than $\gamma(G)$. The reinforcement number of $G$ is the smallest number of edges whose addition to $G$ results in a graph with smaller domination number than $\gamma(G)$. In 2012, Hu and Xu proved that the decision problems for the bondage, the total bondage, the reinforcement and the total reinforcement numbers are all NP-hard in general graphs. In this paper, we improve these results to bipartite graphs.Comment: 13 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:1109.1657; and text overlap with arXiv:1204.4010 by other author