Hidden Symmetries of Higher Dimensional Black Holes and Uniqueness of the Kerr-NUT-(A)dS spacetime

We prove that the most general solution of the Einstein equations with the cosmological constant which admits a principal conformal Killing-Yano tensor is the Kerr-NUT-(A)dS metric. Even when the Einstein equations are not imposed, any spacetime admitting such hidden symmetry can be written in a canonical form which guarantees the following properties: it is of the Petrov type D, it allows the separation of variables for the Hamilton-Jacobi, Klein-Gordon, and Dirac equations, the geodesic motion in such a spacetime is completely integrable. These results naturally generalize the results obtained earlier in four dimensions.Comment: 5 pages, no figure

AC Hopping Magnetotransport Across the Spin Flop Transition in Lightly Doped La_2CuO_4

The weak ferromagnetism present in insulating La_{2}CuO_4 at low doping leads to a spin flop transition, and to transverse (interplane) hopping of holes in a strong external magnetic field. This results in a dimensional crossover 2D $\to$ 3D for the in-plane transport, which in turn leads to an increase of the hole's localization length and increased conduction. We demonstrate theoretically that as a consequence of this mechanism, a frequency-dependent jump of the in-plane ac hopping conductivity occurs at the spin flop transition. We predict the value and the frequency dependence of the jump. Experimental studies of this effect would provide important confirmation of the emerging understanding of lightly doped insulating La_{2-x}Sr_xCuO_4.Comment: 4 pages, 1 figur

Negative Hopping Magnetoresistance and Dimensional Crossover in Lightly Doped Cuprate Superconductors

We show that, due to the weak ferromagnetism of La$_{2-x}$Sr$_x$CuO$_4$, an external magnetic field leads to a dimensional crossover 2D $\to$ 3D for the in-plane transport. The crossover results in an increase of the hole's localization length and hence in a dramatic negative magnetoresistance in the variable range hopping regime. This mechanism quantitatively explains puzzling experimental data on the negative magnetoresistance in the N\'eel phase of La$_{2-x}$Sr$_x$CuO$_4$.Comment: 6 pages, 3 figures; published versio

c-Src drives intestinal regeneration and transformation

The non‐receptor tyrosine kinase c‐Src, hereafter referred to as Src, is overexpressed or activated in multiple human malignancies. There has been much speculation about the functional role of Src in colorectal cancer (CRC), with Src amplification and potential activating mutations in up to 20% of the human tumours, although this has never been addressed due to multiple redundant family members. Here, we have used the adult <i>Drosophila</i> and mouse intestinal epithelium as paradigms to define a role for Src during tissue homeostasis, damage‐induced regeneration and hyperplasia. Through genetic gain and loss of function experiments, we demonstrate that Src is necessary and sufficient to drive intestinal stem cell (ISC) proliferation during tissue self‐renewal, regeneration and tumourigenesis. Surprisingly, Src plays a non‐redundant role in the mouse intestine, which cannot be substituted by the other family kinases Fyn and Yes. Mechanistically, we show that Src drives ISC proliferation through upregulation of EGFR and activation of Ras/MAPK and Stat3 signalling. Therefore, we demonstrate a novel essential role for Src in intestinal stem/progenitor cell proliferation and tumourigenesis initiation <i>in vivo.</i&gt

Screening of Coulomb Impurities in Graphene

We calculate exactly the vacuum polarization charge density in the field of a subcritical Coulomb impurity, $Z|e|/r$, in graphene. Our analysis is based on the exact electron Green's function, obtained by using the operator method, and leads to results that are exact in the parameter $Z\alpha$, where $\alpha$ is the "fine structure constant" of graphene. Taking into account also electron-electron interactions in the Hartree approximation, we solve the problem self-consistently in the subcritical regime, where the impurity has an effective charge $Z_{eff}$, determined by the localized induced charge. We find that an impurity with bare charge Z=1 remains subcritical, $Z_{eff} \alpha < 1/2$, for any $\alpha$, while impurities with $Z=2,3$ and higher can become supercritical at certain values of $\alpha$.Comment: 4 pages, 2 figure

1/N Expansion in Correlated Graphene

We examine the 1/N expansion, where N is the number of two-component Dirac fermions, for Coulomb interactions in graphene with a gap of magnitude $\Delta = 2 m$. We find that for $N\alpha\gg1$, where $\alpha$ is graphene's "fine structure constant", there is a crossover as a function of distance $r$ from the usual 3D Coulomb law, $V(r) \sim 1/r$, to a 2D Coulomb interaction, $V(r) \sim \ln(N\alpha/mr)$, for $m^{-1} \ll r \ll m^{-1} N \alpha/6$. This effect reflects the weak "confinement" of the electric field in the graphene plane. The crossover also leads to unusual renormalization of the quasiparticle velocity and gap at low momenta. We also discuss the differences between the interaction potential in gapped graphene and usual QED for different coupling regimes.Comment: 7 pages, 2 figures; expanded presentation, references adde

Parallel-propagated frame along null geodesics in higher-dimensional black hole spacetimes

In [arXiv:0803.3259] the equations describing the parallel transport of orthonormal frames along timelike (spacelike) geodesics in a spacetime admitting a non-degenerate principal conformal Killing-Yano 2-form h were solved. The construction employed is based on studying the Darboux subspaces of the 2-form F obtained as a projection of h along the geodesic trajectory. In this paper we demonstrate that, although slightly modified, a similar construction is possible also in the case of null geodesics. In particular, we explicitly construct the parallel-transported frames along null geodesics in D=4,5,6 Kerr-NUT-(A)dS spacetimes. We further discuss the parallel transport along principal null directions in these spacetimes. Such directions coincide with the eigenvectors of the principal conformal Killing-Yano tensor. Finally, we show how to obtain a parallel-transported frame along null geodesics in the background of the 4D Plebanski-Demianski metric which admits only a conformal generalization of the Killing-Yano tensor.Comment: 17 pages, no figure

Stationary strings near a higher-dimensional rotating black hole

We study stationary string configurations in a space-time of a higher-dimensional rotating black hole. We demonstrate that the Nambu-Goto equations for a stationary string in the 5D Myers-Perry metric allow a separation of variables. We present these equations in the first-order form and study their properties. We prove that the only stationary string configuration which crosses the infinite red-shift surface and remains regular there is a principal Killing string. A worldsheet of such a string is generated by a principal null geodesic and a timelike at infinity Killing vector field. We obtain principal Killing string solutions in the Myers-Perry metrics with an arbitrary number of dimensions. It is shown that due to the interaction of a string with a rotating black hole there is an angular momentum transfer from the black hole to the string. We calculate the rate of this transfer in a spacetime with an arbitrary number of dimensions. This effect slows down the rotation of the black hole. We discuss possible final stationary configurations of a rotating black hole interacting with a string.Comment: 13 pages, contains additianal material at the end of Section 8, also small misprints are correcte

Analysing Molecular Mechanism Related to Therapy- Resistance in In-vitro Models of Ovarian Cancer

Ovarian cancer is among the most common cause of cancer death and ranks first in the number of deaths each year in the field of gynaecological malignancies. This is due to its late diagnosis and the development of chemoresistance. Platinum derivates, including cisplatinum and carboplatin in combination with paclitaxel, are the first-line chemotherapeutic agents. Platinum derivates irreversibly intercalates into the DNA and creates inter- and intra-strand DNA cross-links. During cell division, platinum-DNA-adducts block the replication machinery, inducing DNA damage and apoptosis. Nearly all patients respond to first-line chemotherapy before it comes later to recurrence of the disease. At time of recurrence, tumours are usually more aggressive, form metastasis in secondary tissues and acquire resistance to conventional chemotherapeutics. Drug resistance is a common problem in tumour therapy not only restricted to ovarian cancer. It is characterized by gene mutations, increased DNA repair, reduced drug efficacy and enhanced drug clearance and detoxification. Up to now the complex molecular mechanism of chemoresistance is not well understood. Increasing evidence points towards AKT over-expression and alteration of the PI3K/AKT/mTOR cascade as a central mechanistic reason for this resistance