Fluctuations and correlations in population models with age structure

We study the population profile in a simple discrete time model of population dynamics. Our model, which is closely related to certain ``bit-string'' models of evolution, incorporates competition for resources via a population dependent death probability, as well as a variable reproduction probability for each individual as a function of age. We first solve for the steady-state of the model in mean field theory, before developing analytic techniques to compute Gaussian fluctuation corrections around the mean field fixed point. Our computations are found to be in good agreement with Monte-Carlo simulations. Finally we discuss how similar methods may be applied to fluctuations in continuous time population models.Comment: 4 page

Limits on Clouds and Hazes for the TRAPPIST-1 Planets

The TRAPPIST-1 planetary system is an excellent candidate for study of the evolution and habitability of M-dwarf planets. Transmission spectroscopy observations performed with the Hubble Space Telescope (HST) suggest the innermost five planets do not possess clear hydrogen atmospheres. Here we reassess these conclusions with recently updated mass constraints and expand the analysis to include limits on metallicity, cloud top pressure, and the strength of haze scattering. We connect recent laboratory results of particle size and production rate for exoplanet hazes to a one-dimensional atmospheric model for TRAPPIST-1 transmission spectra. Doing so, we obtain a physically-based estimate of haze scattering cross sections. We find haze scattering cross sections on the order of 1e-26 to 1e-19 cm squared are needed in hydrogen-rich atmospheres for TRAPPIST-1 d, e, and f to match the HST data. For TRAPPIST-1 g, we cannot rule out a clear hydrogen-rich atmosphere. We also modeled the effects an opaque cloud deck and substantial heavy element content have on the transmission spectra. We determine that hydrogen-rich atmospheres with high altitude clouds, at pressures of 12mbar and lower, are consistent with the HST observations for TRAPPIST-1 d and e. For TRAPPIST-1 f and g, we cannot rule out clear hydrogen-rich cases to high confidence. We demonstrate that metallicities of at least 60xsolar with tropospheric (0.1 bar) clouds agree with observations. Additionally, we provide estimates of the precision necessary for future observations to disentangle degeneracies in cloud top pressure and metallicity. Our results suggest secondary, volatile-rich atmospheres for the outer TRAPPIST-1 planets d, e, and f.Comment: 15 pages, 3 figures, 2 tables, accepted in the Astronomical Journa

Functional characterization of synthetic leukotriene B and its stereochemical isomers.

Leukotriene B (LTB), a potent lipid chemotactic factor for neutrophils, is 5S,12R-dihydroxy-6,14-cis,8,10-trans-eicosatetraenoic acid (Fig 1), based upon direct comparison of natural LTB with synthetic 5S,12R-dihydroxy-6,8,10,14-eicosatetraenoic acid (5,12-di-HETE) stereoisomers in three biological assays. Of the six synthetic stereoisomers evaluated, only the 5S,12R,6,14-cis,8,10-trans compound had chemotactic potency for human neutrophils in vitro that was comparable to that of natural LTB, with a concentration of 3 X 10(9-9) M eliciting a one-half maximum response. In contrast, the racemic mixture of 5R,12R- and 5S,12S-6,10-trans,8,14-cis, the racemic mixture of 5S,12R- and 5R,12S-6,10-trans,8,14-cis, the 5S,12R-6,8-trans,10,14-cis, the 5S,12R-6,8,10-trans,14-cis, and the 5S,12S-6,8,10-trans,14-cis stereoisomers required concentrations of 3 X 10(-7) to 1 X 10(-6) M to elicit comparable responses. Only natural LTB and its synthetic counterpart elicited a local neutrophil infiltration when injected into the skin of the rhesus monkey at 10 ng and 100 ng per site. Natural and synthetic LTB at a concentration of 3 X 10(-8) M each provoked an EC25 contractile response of guinea pig pulmonary parenchymal strips in vitro, whereas the other four tested stereoisomers of 5,12-di-HETE were inactive at this concentration. Structure-function analyses suggest that the neutrophil chemotactic activity depends critically upon the C-1 to C-12 domain, including the stereochemistry of the 6-,8-,and 10-olefinic bonds and the presence of both hydroxyl groups

Knizhnik-Zamolodchikov-type equations for gauged WZNW models

We study correlation functions of coset constructions by utilizing the method of gauge dressing. As an example we apply this method to the minimal models and to the Witten 2D black hole. We exhibit a striking similarity between the latter and the gravitational dressing. In particular, we look for logarithmic operators in the 2D black hole.Comment: 24 pages, latex, no figures. More discussion of logarithmic operators was adde

3-dimensional Gravity from the Turaev-Viro Invariant

We study the $q$-deformed su(2) spin network as a 3-dimensional quantum gravity model. We show that in the semiclassical continuum limit the Turaev-Viro invariant obtained recently defines naturally regularized path-integral $\grave{\rm a}$ la Ponzano-Regge, In which a contribution from the cosmological term is effectively included. The regularization dependent cosmological constant is found to be ${4\pi^2\over k^2} +O(k^{-4})$, where $q^{2k}=1$. We also discuss the relation to the Euclidean Chern-Simons-Witten gravity in 3-dimension.Comment: 11page