Polar bulges and polar nuclear discs: the case of NGC 4698

The early-type spiral NGC 4698 is known to host a nuclear disc of gas and stars which is rotating perpendicularly with respect to the galaxy main disc. In addition, the bulge and main disc are characterised by a remarkable geometrical decoupling. Indeed they appear elongated orthogonally to each other. In this work the complex structure of the galaxy is investigated by a detailed photometric decomposition of optical and near-infrared images. The intrinsic shape of the bulge was constrained from its apparent ellipticity, its twist angle with respect to the major axis of the main disc, and the inclination of the main disc. The bulge is actually elongated perpendicular to the main disc and it is equally likely to be triaxial or axisymmetric. The central surface brightness, scalelength, inclination, and position angle of the nuclear disc were derived by assuming it is infinitesimally thin and exponential. Its size, orientation, and location do not depend on the observed passband. These findings support a scenario in which the nuclear disc is the end result of the acquisition of external gas by the pre-existing triaxial bulge on the principal plane perpendicular to its shortest axis and perpendicular to the galaxy main disc. The subsequent star formation either occurred homogeneously all over the extension of the nuclear disc or through an inside-out process that ended more than 5 Gyr ago.Comment: 6 pages, 3 figures. Accepted for publication in MNRAS Letter

Large N expansion of the 2-matrix model

We present a method, based on loop equations, to compute recursively all the terms in the large $N$ topological expansion of the free energy for the 2-hermitian matrix model. We illustrate the method by computing the first subleading term, i.e. the free energy of a statistical physics model on a discretized torus.Comment: 41 pages, 9 figures eps

Mixed correlation function and spectral curve for the 2-matrix model

We compute the mixed correlation function in a way which involves only the orthogonal polynomials with degrees close to $n$, (in some sense like the Christoffel Darboux theorem for non-mixed correlation functions). We also derive new representations for the differential systems satisfied by the biorthogonal polynomials, and we find new formulae for the spectral curve. In particular we prove the conjecture of M. Bertola, claiming that the spectral curve is the same curve which appears in the loop equations.Comment: latex, 1 figure, 55 page

Loop equations for the semiclassical 2-matrix model with hard edges

The 2-matrix models can be defined in a setting more general than polynomial potentials, namely, the semiclassical matrix model. In this case, the potentials are such that their derivatives are rational functions, and the integration paths for eigenvalues are arbitrary homology classes of paths for which the integral is convergent. This choice includes in particular the case where the integration path has fixed endpoints, called hard edges. The hard edges induce boundary contributions in the loop equations. The purpose of this article is to give the loop equations in that semicassical setting.Comment: Latex, 20 page

Spectra of random Hermitian matrices with a small-rank external source: supercritical and subcritical regimes

Random Hermitian matrices with a source term arise, for instance, in the study of non-intersecting Brownian walkers \cite{Adler:2009a, Daems:2007} and sample covariance matrices \cite{Baik:2005}. We consider the case when the $n\times n$ external source matrix has two distinct real eigenvalues: $a$ with multiplicity $r$ and zero with multiplicity $n-r$. The source is small in the sense that $r$ is finite or $r=\mathcal O(n^\gamma)$, for $0< \gamma<1$. For a Gaussian potential, P\'ech\'e \cite{Peche:2006} showed that for $|a|$ sufficiently small (the subcritical regime) the external source has no leading-order effect on the eigenvalues, while for $|a|$ sufficiently large (the supercritical regime) $r$ eigenvalues exit the bulk of the spectrum and behave as the eigenvalues of $r\times r$ Gaussian unitary ensemble (GUE). We establish the universality of these results for a general class of analytic potentials in the supercritical and subcritical regimes.Comment: 41 pages, 4 figure

High Glucose Impairs Expression and Activation of MerTK in ARPE-19 Cells

MerTK (Mer Tyrosine Kinase) is a cell surface receptor that regulates phagocytosis of pho-toreceptor outer segments (POS) in retinal pigment epithelial (RPE) cells. POS phagocytosis is im-paired in several pathologies, including diabetes. In this study, we investigate whether hyperglyce-mic conditions may affect MerTK expression and activation in ARPE-19 cells, a retinal pigment epithelial cellular model. ARPE-19 cells were cultured in standard (CTR) or high-glucose (HG) me-dium for 24 h. Then, we analyzed: mRNA levels and protein expression of MerTK and ADAM9, a protease that cleaves the extracellular region of MerTK; the amount of cleaved Mer (sMer); and the ability of GAS6, a MerTK ligand, to induce MerTK phosphorylation. Since HG reduces miR-126 levels, and ADAM9 is a target of miR-126, ARPE-19 cells were transfected with miR-126 inhibitor or mimic; then, we evaluated ADAM9 expression, sMer, and POS phagocytosis. We found that HG reduced expression and activation of MerTK. Contextually, HG increased expression of ADAM9 and the amount of sMer. Overexpression of miR-126 reduced levels of sMer and improved phago-cytosis in ARPE-19 cells cultured with HG. In this study, we demonstrate that HG compromises MerTK expression and activation in ARPE-19 cells. Our results suggest that HG up-regulates ADAM9 expression, leading to increased shedding of MerTK. The consequent rise in sMer coupled to reduced expression of MerTK impairs binding and internalization of POS in ARPE-19 cells

A holographic reduction of Minkowski space-time

Minkowski space can be sliced, outside the lightcone, in terms of Euclidean Anti-de Sitter and Lorentzian de Sitter slices. In this paper we investigate what happens when we apply holography to each slice separately. This yields a dual description living on two spheres, which can be interpreted as the boundary of the light cone. The infinite number of slices gives rise to a continuum family of operators on the two spheres for each separate bulk field. For a free field we explain how the Green's function and (trivial) S-matrix in Minkowski space can be reconstructed in terms of two-point functions of some putative conformal field theory on the two spheres. Based on this we propose a Minkowski/CFT correspondence which can also be applied to interacting fields. We comment on the interpretation of the conformal symmetry of the CFT, and on generalizations to curved space.Comment: 47 pages, latex, 2 figures; v2: discussion of translations added, final version to appear in Nucl.Phys.

Inverse problems associated with integrable equations of Camassa-Holm type; explicit formulas on the real axis, I

The inverse problem which arises in the Camassa--Holm equation is revisited for the class of discrete densities. The method of solution relies on the use of orthogonal polynomials. The explicit formulas are obtained directly from the analysis on the real axis without any additional transformation to a "string" type boundary value problem known from prior works

Wightman Functions' Behaviour on the Event Horizon of an Extremal Reissner-Nordstr\"om Black Hole

A weaker Haag, Narnhofer and Stein prescription as well as a weaker Hessling Quantum Equivalence Principle for the behaviour of thermal Wightman functions on an event horizon are analysed in the case of an extremal Reissner-Nordstr\"{o}m black hole in the limit of a large mass. In order to avoid the degeneracy of the metric in the stationary coordinates on the horizon, a method is introduced which employs the invariant length of geodesics which pass the horizon. First the method is checked for a massless scalar field on the event horizon of the Rindler wedge, extending the original procedure of Haag, Narnhofer and Stein onto the {\em whole horizon} and recovering the same results found by Hessling. Afterwards the HNS prescription and Hessling's prescription for a massless scalar field are analysed on the whole horizon of an extremal Reissner-Nordstr\"{o}m black hole in the limit of a large mass. It is proved that the weak form of the HNS prescription is satisfyed for all the finite values of the temperature of the KMS states, i.e., this principle does not determine any Hawking temperature. It is found that the Reissner-Nordstr\"{o}m vacuum, i.e., $T=0$ does satisfy the weak HNS prescription and it is the only state which satisfies weak Hessling's prescription, too. Finally, it is suggested that all the previously obtained results should be valid dropping the requirements of a massless field and of a large mass black hole.Comment: 27 pages, standard LaTex, no figures, final version containing the results following from Hessling's principle as they appeared in the other paper gr-qc/9510016, minor changes in the text and in references, it will appear on Class. Quant. Gra