Numerical investigation of the dynamics of linear spin ss fields on Kerr background I. Late time tails of spin s=±1,±2s = \pm 1, \pm 2 fields

The time evolution of linear fields of spin $s = \pm 1$ and $s = \pm 2$ on Kerr black hole spacetimes are investigated by solving the homogeneous Teukolsky equation numerically. The applied numerical setup is based on a combination of conformal compactification and the hyperbolic initial value problem. The evolved basic variables are expanded in terms of spin-weighted spherical harmonics which allows us to evaluate all the angular derivatives analytically, whereas the evolution of the expansion coefficients, in the time-radial section, is determined by applying the method of lines implemented in a fourth order accurate finite differencing stencil. Concerning the initialization, in all of our investigations single mode excitations---either static or purely dynamical type initial data---are applied. Within this setup the late time tail behavior is investigated. Due to the applied conformal compactification the asymptotic decay rates are determined at three characteristic locations---in the domain of outer communication, at the event horizon and at future null infinity---simultaneously. Recently introduced new type of `energy' and `angular momentum' balance relations are also applied in order to demonstrate the feasibility and robustness of the developed numerical schema, and also to verify the proper implementation of the underlying mathematical model.Comment: 38 pages, 5 figures, typos correcte

On a strong version of the Kepler conjecture

We raise and investigate the following problem that one can regard as a very close relative of the densest sphere packing problem. If the Euclidean 3-space is partitioned into convex cells each containing a unit ball, how should the shapes of the cells be designed to minimize the average surface area of the cells? In particular, we prove that the average surface area in question is always at least 13.8564... .Comment: 9 page

A glükokortikoidok hatását és metabolizmusát befolyásoló gén-polimorfizmusok patofiziológiai szerepének vizsgálata = Pathophysiological significance of gene polymorphisms affecting glucocorticoid action and metabolism

A HSD11B1 génen in silico kutatásainkkal azonosított 65 polimorfizmus közül - transzkripciós faktorok kötőhelyein elhelyezkedésük alapján - 12 polimorfizmust részletesen vizsgáltunk és meghatároztuk populáció-szintű gyakoriságukat. A vizsgált 12 polimorfizmus közül a rs4844880 polimorf allél bizonyult kiemelten jelentősnek; a polimorfizmus hordozása kedvezőbb csont ásványianyag tartalommal (BMC) társult és jelenléte esetén Cushing-szindrómás betegekben magasabb szérum kortizol és osteokalcin koncentrációkat detektáltunk. Kimutattuk, hogy a polimorf allélt tartalmazó vektorral transzfektált Hela sejtek csökkent luciferáz aktivitást mutattak, ami magyarázza a rs4844880 allél hordozás csontanyagcserére kifejtett kedvező hatását. A GR gén 4 polimorfizmusának (Bcl1, N363S, ER22/23EK és A3669G) vizsgálatával kimutattuk, hogy a Bcl1 polimorfizmus jelenléte csökkent BMC értékkel társul Cushing-szindrómás betegekben. Kimutattuk továbbá, hogy várandós nőkben a Bcl1 polimorfizmus hordozása kockázati tényező a HELLP szindróma kialakulásában, és az ER22/23EK polimorfizmus jelenléte várandós nőkben csökkenti a graviditás alatti testsúly növekedés kockázatát. Mindezek az eredmények új adatokkal egészítik ki a glükokortikoidok iránti érzékenység pathofiziológiai jelentőségét, melyet nagyrészt genetikai tényezők, köztük elsősorban a HSD11B1 és GR gének variánsai határoznak meg. | Of the 65 polymorphisms identified in the HSD11B1 gene using our in silico analysis, 12 were further investigated based on their critical locations in sites which bind transcription factors, and their allelic frequencies were determined in healthy subjects. Of these 12 polymorphic alleles, the rs4844880 proved to be particularly important, because this polymorphic allele was associated with better bone mineral content (BMC) and, in patients with Cushing’s syndrome, with higher serum cortisol and osteocalcin concentrations. Hela cells transfected with this polymorphic variant showed decreased luciferase activity compared to those transfected with the wild-type variant, thus explaining the beneficial effect of the rs4844880 polymorphism on bone metabolism. Studies on the 4 polymorphisms of the GR gene (Bcl1, N363S, ER22/23EK and A3669G) indicated that the polymorphic Bcl1 allele was associated with a lower bone mineral content in patients with Cushing’s syndrome. In addition, we showed that the presence of this allele is a risk factor for HELLP syndrome in pregnant women, and that carriers of the ER22/23/EK polymorphism have a lower risk for weight gain during pregnancy. All these finding provide novel data on the pathophysiologic significance of glucocorticoid sensitivity, determined by genetic factors mainly including the HSD11B1 and GR gene variants

Estimation of influential points in any data set from coefficient of determination and its leave-one-out cross-validated counterpart

Coefficient of determination (R2) and its leave-one-out cross-validated analogue (denoted by Q2 or Rcv 2) are the most frequantly published values to characterize the predictive performance of models. In this article we use R2 and Q2 in a reversed aspect to determine uncommon points, i.e. influential points in any data sets. The term (1 - Q2)/(1 - R2) corresponds to the ratio of predictive residual sum of squares and the residual sum of squares. The ratio correlates to the number of influential points in experimental and random data sets. We propose an (approximate) F test on (1 - Q2)/(1 - R2) term to quickly pre-estimate the presence of influential points in training sets of models. The test is founded upon the routinely calculated Q2 and R2 values and warns the model builders to verify the training set, to perform influence analysis or even to change to robust modeling. Graphical Abstract: [Figure not available: see fulltext.] © 2013 Springer Science+Business Media Dordrecht