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    Distribution of interstitial stem cells in Hydra

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    The distribution of interstitial stem cells along the Hydra body column was determined using a simplified cloning assay. The assay measures stem cells as clone-forming units (CFU) in aggregates of nitrogen mustard inactivated Hydra tissue. The concentration of stem cells in the gastric region was uniform at about 0.02 CFU/epithelial cell. In both the hypostome and basal disk the concentration was 20-fold lower. A decrease in the ratio of stem cells to committed nerve and nematocyte precursors was correlated with the decrease in stem cell concentration in both hypostome and basal disk. The ratio of stem cells to committed precursors is a sensitive indicator of the rate of self-renewal in the stem cell population. From the ratio it can be estimated that <10% of stem cells self-renew in the hypostome and basal disk compared to 60% in the gastric region. Thus, the results provide an explanation for the observed depletion of stem cells in these regions. The results also suggest that differentiation and self-renewal compete for the same stem cell population

    Tilting Jupiter (a bit) and Saturn (a lot) During Planetary Migration

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    We study the effects of planetary late migration on the gas giants obliquities. We consider the planetary instability models from Nesvorny & Morbidelli (2012), in which the obliquities of Jupiter and Saturn can be excited when the spin-orbit resonances occur. The most notable resonances occur when the s7s_7 and s8s_8 frequencies, changing as a result of planetary migration, become commensurate with the precession frequencies of Jupiter's and Saturn's spin vectors. We show that Jupiter may have obtained its present obliquity by crossing of the s8s_8 resonance. This would set strict constrains on the character of migration during the early stage. Additional effects on Jupiter's obliquity are expected during the last gasp of migration when the s7s_7 resonance was approached. The magnitude of these effects depends on the precise value of the Jupiter's precession constant. Saturn's large obliquity was likely excited by capture into the s8s_8 resonance. This probably happened during the late stage of planetary migration when the evolution of the s8s_8 frequency was very slow, and the conditions for capture into the spin-orbit resonance with s8s_8 were satisfied. However, whether or not Saturn is in the spin-orbit resonance with s8s_8 at the present time is not clear, because the existing observations of Saturn's spin precession and internal structure models have significant uncertainties.Comment: 29 pages, 8 figures, accepted for publication in The Astrophysical Journa

    Upper and lower bounds on resonances for manifolds hyperbolic near infinity

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    For a conformally compact manifold that is hyperbolic near infinity and of dimension n+1n+1, we complete the proof of the optimal O(rn+1)O(r^{n+1}) upper bound on the resonance counting function, correcting a mistake in the existing literature. In the case of a compactly supported perturbation of a hyperbolic manifold, we establish a Poisson formula expressing the regularized wave trace as a sum over scattering resonances. This leads to an rn+1r^{n+1} lower bound on the counting function for scattering poles.Comment: 29 pages, minor corrections, added one figur
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