1,282 research outputs found

    Inverting the Sachs-Wolfe Formula: an Inverse Problem Arising in Early-Universe Cosmology

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    The (ordinary) Sachs-Wolfe effect relates primordial matter perturbations to the temperature variations δT/T\delta T/T in the cosmic microwave background radiation; δT/T\delta T/T can be observed in all directions around us. A standard but idealised model of this effect leads to an infinite set of moment-like equations: the integral of P(k)j2(ky)P(k) j_\ell^2(ky) with respect to k (0<k<0<k<\infty) is equal to a given constant, CC_\ell, for =0,1,2,...\ell=0,1,2,.... Here, P is the power spectrum of the primordial density variations, jj_\ell is a spherical Bessel function and y is a positive constant. It is shown how to solve these equations exactly for ~P(k)P(k). The same solution can be recovered, in principle, if the first ~m equations are discarded. Comparisons with classical moment problems (where j2(ky)j_\ell^2(ky) is replaced by kk^\ell) are made.Comment: In Press Inverse Problems 1999, 15 pages, 0 figures, Late

    Body Condition of Endangered Humpback Chub in Relation to Temperature and Discharge in the Lower Colorado River

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    Determining the population status of endangered Humpback Chub Gila cypha is a major component of the adaptive management program designed to inform operation of Glen Canyon Dam upstream from Grand Canyon, Arizona. In recent decades, resource managers have identified a portfolio of management actions (with intermittent implementation) to promote population recovery of Humpback Chub, including nonnative fish removal, changes in water release volumes and discharge ramping schedules, and reductions in hydropower peaking operations. The Humpback Chub population in Grand Canyon has increased over this same period, causal factors for which are unclear. We took advantage of unusual hydrology in the Colorado River basin in 2011 to assess trends in juvenile Humpback Chub length–weight relationships and condition in the Colorado River below Glen Canyon Dam as well as in the unregulated Little Colorado River. Within each river, we observed higher length–weight b-parameter estimates (exponent of the standard power equation) at higher water temperatures. We also found higher slope estimates for the length–weight relationship at higher temperatures in the Little Colorado River. Slope estimates were more variable in the Colorado River, where mean water temperatures were more uniform. The next step is to examine whether Humpback Chub length–weight relationships influence population metrics such as abundance or survival. If these relationships exist, then monitoring condition in juvenile Humpback Chub would provide a quick and low-cost technique for assessing population response to planned management experiments or changing environmental conditions

    Expression profiles for macrophage alternative activation genes in AD and in mouse models of AD.

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    BACKGROUND: Microglia are associated with neuritic plaques in Alzheimer disease (AD) and serve as a primary component of the innate immune response in the brain. Neuritic plaques are fibrous deposits composed of the amyloid beta-peptide fragments (Abeta) of the amyloid precursor protein (APP). Numerous studies have shown that the immune cells in the vicinity of amyloid deposits in AD express mRNA and proteins for pro-inflammatory cytokines, leading to the hypothesis that microglia demonstrate classical (Th-1) immune activation in AD. Nonetheless, the complex role of microglial activation has yet to be fully explored since recent studies show that peripheral macrophages enter an "alternative" activation state. METHODS: To study alternative activation of microglia, we used quantitative RT-PCR to identify genes associated with alternative activation in microglia, including arginase I (AGI), mannose receptor (MRC1), found in inflammatory zone 1 (FIZZ1), and chitinase 3-like 3 (YM1). RESULTS: Our findings confirmed that treatment of microglia with anti-inflammatory cytokines such as IL-4 and IL-13 induces a gene profile typical of alternative activation similar to that previously observed in peripheral macrophages. We then used this gene expression profile to examine two mouse models of AD, the APPsw (Tg-2576) and Tg-SwDI, models for amyloid deposition and for cerebral amyloid angiopathy (CAA) respectively. AGI, MRC1 and YM1 mRNA levels were significantly increased in the Tg-2576 mouse brains compared to age-matched controls while TNFalpha and NOS2 mRNA levels, genes commonly associated with classical activation, increased or did not change, respectively. Only TNFalpha mRNA increased in the Tg-SwDI mouse brain. Alternative activation genes were also identified in brain samples from individuals with AD and were compared to age-matched control individuals. In AD brain, mRNAs for TNFalpha, AGI, MRC1 and the chitinase-3 like 1 and 2 genes (CHI3L1; CHI3L2) were significantly increased while NOS2 and IL-1beta mRNAs were unchanged. CONCLUSION: Immune cells within the brain display gene profiles that suggest heterogeneous, functional phenotypes that range from a pro-inflammatory, classical activation state to an alternative activation state involved in repair and extracellular matrix remodeling. Our data suggest that innate immune cells in AD may exhibit a hybrid activation state that includes characteristics of classical and alternative activation

    Resonance regimes of scattering by small bodies with impedance boundary conditions

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    The paper concerns scattering of plane waves by a bounded obstacle with complex valued impedance boundary conditions. We study the spectrum of the Neumann-to-Dirichlet operator for small wave numbers and long wave asymptotic behavior of the solutions of the scattering problem. The study includes the case when k=0k=0 is an eigenvalue or a resonance. The transformation from the impedance to the Dirichlet boundary condition as impedance grows is described. A relation between poles and zeroes of the scattering matrix in the non-self adjoint case is established. The results are applied to a problem of scattering by an obstacle with a springy coating. The paper describes the dependence of the impedance on the properties of the material, that is on forces due to the deviation of the boundary of the obstacle from the equilibrium position
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