Solving the Dirac equation with nonlocal potential by Imaginary Time Step method

The Imaginary Time Step (ITS) method is applied to solve the Dirac equation with the nonlocal potential in coordinate space by the ITS evolution for the corresponding Schr\"odinger-like equation for the upper component. It is demonstrated that the ITS evolution can be equivalently performed for the Schr\"odinger-like equation with or without localization. The latter algorithm is recommended in the application for the reason of simplicity and efficiency. The feasibility and reliability of this algorithm are also illustrated by taking the nucleus $^{16}$O as an example, where the same results as the shooting method for the Dirac equation with localized effective potentials are obtained

Spontaneous γH2AX Foci in Human Solid Tumor-Derived Cell Lines in Relation to p21WAF1 and WIP1 Expression.

Phosphorylation of H2AX on Ser139 (γH2AX) after exposure to ionizing radiation produces nuclear foci that are detectable by immunofluorescence microscopy. These so-called γH2AX foci have been adopted as quantitative markers for DNA double-strand breaks. High numbers of spontaneous γH2AX foci have also been reported for some human solid tumor-derived cell lines, but the molecular mechanism(s) for this response remains elusive. Here we show that cancer cells (e.g., HCT116; MCF7) that constitutively express detectable levels of p21WAF1 (p21) exhibit low numbers of γH2AX foci (<3/nucleus), whereas p21 knockout cells (HCT116p21-/-) and constitutively low p21-expressing cells (e.g., MDA-MB-231) exhibit high numbers of foci (e.g., >50/nucleus), and that these foci are not associated with apoptosis. The majority (>95%) of cells within HCT116p21-/- and MDA-MB-231 cultures contain high levels of phosphorylated p53, which is localized in the nucleus. We further show an inverse relationship between γH2AX foci and nuclear accumulation of WIP1, an oncogenic phosphatase. Our studies suggest that: (i) p21 deficiency might provide a selective pressure for the emergence of apoptosis-resistant progeny exhibiting genomic instability, manifested as spontaneous γH2AX foci coupled with phosphorylation and nuclear accumulation of p53; and (ii) p21 might contribute to positive regulation of WIP1, resulting in dephosphorylation of γH2AX

Multipartite unlockable bound entanglement in the stabilizer formalism

We find an interesting relationship between multipartite bound entangled states and the stabilizer formalism. We prove that if a set of commuting operators from the generalized Pauli group on $n$ qudits satisfy certain constraints, then the maximally mixed state over the subspace stabilized by them is an unlockable bound entangled state. Moreover, the properties of this state, such as symmetry under permutations of parties, undistillability and unlockability, can be easily explained from the stabilizer formalism without tedious calculation. In particular, the four-qubit Smolin state and its recent generalization to even number of qubits can be viewed as special examples of our results. Finally, we extend our results to arbitrary multipartite systems in which the dimensions of all parties may be different.Comment: 7 pages, no figur

Degeneration and impaired regeneration of gray matter oligodendrocytes in amyotrophic lateral sclerosis.

Oligodendrocytes associate with axons to establish myelin and provide metabolic support to neurons. In the spinal cord of amyotrophic lateral sclerosis (ALS) mice, oligodendrocytes downregulate transporters that transfer glycolytic substrates to neurons and oligodendrocyte progenitors (NG2(+) cells) exhibit enhanced proliferation and differentiation, although the cause of these changes in oligodendroglia is unknown. We found extensive degeneration of gray matter oligodendrocytes in the spinal cord of SOD1 (G93A) ALS mice prior to disease onset. Although new oligodendrocytes were formed, they failed to mature, resulting in progressive demyelination. Oligodendrocyte dysfunction was also prevalent in human ALS, as gray matter demyelination and reactive changes in NG2(+) cells were observed in motor cortex and spinal cord of ALS patients. Selective removal of mutant SOD1 from oligodendroglia substantially delayed disease onset and prolonged survival in ALS mice, suggesting that ALS-linked genes enhance the vulnerability of motor neurons and accelerate disease by directly impairing the function of oligodendrocytes

Trade-off between multiple-copy transformation and entanglement catalysis

We demonstrate that multiple copies of a bipartite entangled pure state may serve as a catalyst for certain entanglement transformations while a single copy cannot. Such a state is termed a "multiple-copy catalyst" for the transformations. A trade-off between the number of copies of source state and that of the catalyst is also observed. These results can be generalized to probabilistic entanglement transformations directly.Comment: Essentially the journal version. 7 pages, no figures. Minor correction

Spin waves in the block checkerboard antiferromagnetic phase

Motivated by the discovery of new family 122 iron-based superconductors, we present the theoretical results on the ground state phase diagram, spin wave and dynamic structure factor of the extended $J_{1}-J_{2}$ Heisenberg model. In the reasonable physical parameter region of $K_{2}Fe_{4}Se_{5}$, we fi{}nd the block checkerboard antiferromagnetic order phase is stable. There are two acoustic branches and six optical branches spin wave in the block checkerboard antiferromagnetic phase, which has analytic expression in the high symmetry points. To compare the further neutron scattering experiments, we discuss the saddlepoint structure in the magnetic excitation spectrum and calculate the predicted inelastic neutron scattering pattern based on linear spin wave theory

Enhanced cytosolic delivery and release of CRISPR/Cas9 by black phosphorus nanosheets for genome editing

A biodegradable two-dimensional (2D) delivery platform based on loading black phosphorus nanosheets (BPs) with Cas9 ribonucleoprotein engineered with three nuclear localization signals (NLSs) at C terminus (Cas9N3) is successfully established. The Cas9N3-BPs enter cells effectively via membrane penetration and endocytosis pathways, followed by a BPs biodegradation-associated endosomal escape and cytosolic releases of the loaded Cas9N3 complexes. The Cas9N3-BPs thus provide efficient genome editing and gene silencing in vitro and in vivo at a relatively low dose as compared with other nanoparticle-based delivery platforms. This biodegradable 2D delivery platform offers a versatile cytosolic delivery approach for CRISPR/Cas9 ribonucleoprotein and other bioactive macromolecules for biomedical applications

Dissipation in Quasi One-Dimensional Superconducting Single-Crystal Sn Nanowires

Electrical transport measurements were made on single-crystal Sn nanowires to understand the intrinsic dissipation mechanisms of a one-dimensional superconductor. While the resistance of wires of diameter larger than 70 nm drops precipitately to zero at Tc near 3.7 K, a residual resistive tail extending down to low temperature is found for wires with diameters of 20 and 40 nm. As a function of temperature, the logarithm of the residual resistance appears as two linear sections, one within a few tenths of a degree below Tc and the other extending down to at least 0.47 K, the minimum temperature of the measurements. The residual resistance is found to be ohmic at all temperatures below Tc of Sn. These findings are suggestive of a thermally activated phase slip process near Tc and quantum fluctuation-induced phase slip process in the low temperature regime. When the excitation current exceeds a critical value, the voltage-current (V-I) curves show a series of discrete steps in approaching the normal state. These steps cannot be fully understood with the classical Skocpol-Beasley-Tinkham phase slip center model (PSC), but can be qualitatively accounted for partly by the PSC model modified by Michotte et al.Comment: 7 pages, 5 figures. To be appeared on Physical Review B 71, 200