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

Effect of timing and female quality on clutch size in the Collared Flycatcher Ficedula albicollis

Capsule: Laying date and female age appear to be related to clutch size. Aims: To test two hypotheses ('date' and 'quality'), which might explain why fewer eggs are laid late in the season. Methods: Four years of data and multivariate analysis were used to test the effects of timing of breeding and female quality reflected by morphological variables and age on clutch size in the Collared Flycatcher Ficedula albicollis. We estimated food supply during parental care by measuring diet composition of nestlings. Results: We distinguished the independent effects of date and age of females on clutch size. The type of prey fed to nestlings was different early and late in the season. Hence food supply during the nestling care period may be a limiting environmental factor that indirectly determines clutch size. Conclusion: Our results are consistent with the predictions of the date hypothesis, but the quality hypothesis was also partially supported. Depending on year effects, 30-50% of the variance in clutch size may be related to the timing of breeding and an additional 5-10% may be due to quality (age) differences between early- and late-breeding birds

Separation with restricted families of sets

Given a finite $n$-element set $X$, a family of subsets ${\mathcal F}\subset 2^X$ is said to separate $X$ if any two elements of $X$ are separated by at least one member of $\mathcal F$. It is shown that if $|\mathcal F|>2^{n-1}$, then one can select $\lceil\log n\rceil+1$ members of $\mathcal F$ that separate $X$. If $|\mathcal F|\ge \alpha 2^n$ for some $0<\alpha<1/2$, then $\log n+O(\log\frac1{\alpha}\log\log\frac1{\alpha})$ members of $\mathcal F$ are always sufficient to separate all pairs of elements of $X$ that are separated by some member of $\mathcal F$. This result is generalized to simultaneous separation in several sets. Analogous questions on separation by families of bounded Vapnik-Chervonenkis dimension and separation of point sets in ${\mathbb{R}}^d$ by convex sets are also considered.Comment: 13 page

Az apoptózis és a fagocitózis összefonódása = Link between apoptosis and phagocytosis

Szervezetünkben naponta több 10 millió sejt hal el apoptózissal. Kísérleteinkben azt vizsgáltuk, hogyan hangolódhat össze in vivo az apoptózis és az apoptótikus sejteket eltakarító fagocitózis mértéke. Vizsgáltuk ebben a vonatkozásban egy az in vivo apopto-fagocitózis során mind az elhaló sejtben, mind a makrofágban kifejeződő multifunkcionális fehérje, a transzglutamináz 2 (TG2), a lebomló sejtekből és a fagocitáló makrofágokból is felszabaduló adenozin, és a makrofágok differenciációjában és az apoptózis szabályozásában is szerepet játszó retinoidok szerepét. Megállapítottuk, hogy a TG2 sejtektől függően, különféle biológiai funkcióban segítheti vagy gátolhatja az apoptózist. Elhaló sejtekben és az eltakarító makrofágokban együttesen megjelenve, viszont biztosítja, hogy az apoptózis és az eltakarítás hatékonyan folyjék, és se gyulladás, se szövetkárosodás ne kísérje a folyamatot. A tímusz mint modell szervet tanulmányozva, ahol a képződő timociták 95%-a elhal, bizonyítottuk, hogy mind az adenozin, mind a retinoidok jelen van, és gyorsítja mind a timociták apoptózisát, mind a fagocitózis hatékonyságát. Az adenozin emellett hozzájárul az apoptótikus sejtek gyulladásellenes hatásának csökkentéséhez is. Adataink arra utalnak, hogy vannak közös molekulák az apoptózis és a fagocitózis program szabályozásában, amelyek lehetővé teszik ezek összehangolt működését, és így gyógyszer targetmolekulák lehetnek. | In a human body every day several 10 million cells die by apoptosis. In our experiments it was investigated how is the in vivo rate of apoptosis is balanced by the capacity of the clearance mediated by professional macrophages. In this context the involvement of a multifunctional protein, transglutaminase 2 (TG2) previously shown by us to be coupled to the in vivo apopto-phagocytosis program, that of adenosine released by dying cells and engulfing macrophages, and that of retinoids, known to regulate both apoptosis and macrophage differentiation were investigated. We have shown that TG2 depending on the cell type and using its different biological activities can both promote and inhibit apoptosis. When the protein appears in both apoptotic and phagocytic cells, the protein ensures that both apoptosis and phagocytosis proceeds efficiently, and no tissue injury develops. Using thymus as a model organ, in which 95% of the thymocytes produced die, we have shown that both retinoids and adenosine are present, and accelerate both the apoptosis of nonselected thymocytes and the efficacy of phagocytosis. In addition, adenosine is a soluble mediator that mediates the anti-inflammatory effect of apoptotic cells. Our data demonstrate that there are common regulator molecules in the apoptosis and phagocytosis program that harmonize the two processes, and thus might be potential pharmacological target molecules