180 research outputs found

    Enhancing service mathematics teaching through strategic alignment

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    An interdisciplinary eye on mathematics service teaching

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    The Increasing Necessity of Skills Diversity in Team Teaching

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    Quantum dynamics and thermalization for out-of-equilibrium phi^4-theory

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    The quantum time evolution of \phi^4-field theory for a spatially homogeneous system in 2+1 space-time dimensions is investigated numerically for out-of-equilibrium initial conditions on the basis of the Kadanoff-Baym equations including the tadpole and sunset self-energies. Whereas the tadpole self-energy yields a dynamical mass, the sunset self-energy is responsible for dissipation and an equilibration of the system. In particular we address the dynamics of the spectral (`off-shell') distributions of the excited quantum modes and the different phases in the approach to equilibrium described by Kubo-Martin-Schwinger relations for thermal equilibrium states. The investigation explicitly demonstrates that the only translation invariant solutions representing the stationary fixed points of the coupled equation of motions are those of full thermal equilibrium. They agree with those extracted from the time integration of the Kadanoff-Baym equations in the long time limit. Furthermore, a detailed comparison of the full quantum dynamics to more approximate and simple schemes like that of a standard kinetic (on-shell) Boltzmann equation is performed. Our analysis shows that the consistent inclusion of the dynamical spectral function has a significant impact on relaxation phenomena. The different time scales, that are involved in the dynamical quantum evolution towards a complete thermalized state, are discussed in detail. We find that far off-shell 1 3 processes are responsible for chemical equilibration, which is missed in the Boltzmann limit. Finally, we address briefly the case of (bare) massless fields. For sufficiently large couplings λ\lambda we observe the onset of Bose condensation, where our scheme within symmetric \phi^4-theory breaks down.Comment: 77 pages, 26 figure

    P2Y12 expression and function in alternatively activated human microglia

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    Objective: To investigate and measure the functional significance of altered P2Y12 expression in the context of human microglia activation. Methods: We performed in vitro and in situ experiments to measure how P2Y12 expression can influence disease-relevant functional properties of classically activated (M1) and alternatively activated (M2) human microglia in the inflamed brain. Results: We demonstrated that compared to resting and classically activated (M1) human microglia, P2Y12 expression is increased under alternatively activated (M2) conditions. In response to ADP, the endogenous ligand of P2Y12, M2 microglia have increased ligand-mediated calcium responses, which are blocked by selective P2Y12 antagonism. P2Y12 antagonism was also shown to decrease migratory and inflammatory responses in human microglia upon exposure to nucleotides that are released during CNS injury; no effects were observed in human monocytes or macrophages. In situ experiments confirm that P2Y12 is selectively expressed on human microglia and elevated under neuropathologic conditions that promote Th2 responses, such as parasitic CNS infection. Conclusion: These findings provide insight into the roles of M2 microglia in the context of neuroinflammation and suggest a mechanism to selectively target a functionally unique population of myeloid cells in the CNS

    Critical points on growth curves in autoregressive and mixed models

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    Adjusting autoregressive and mixed models to growth data fits discontinuous functions, which makes it difficult to determine critical points. In this study we propose a new approach to determine the critical stability point of cattle growth using a first-order autoregressive model and a mixed model with random asymptote, using the deterministic portion of the models. Three functions were compared: logistic, Gompertz, and Richards. The Richards autoregressive model yielded the best fit, but the critical growth values were adjusted very early, and for this purpose the Gompertz model was more appropriate
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