354,459 research outputs found

    Nonsmooth and level-resolved dynamics illustrated with the tight binding model

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    We point out that in the first order time-dependent perturbation theory, the transition probability may behave nonsmoothly in time and have kinks periodically. Moreover, the detailed temporal evolution can be sensitive to the exact locations of the eigenvalues in the continuum spectrum, in contrast to coarse-graining ideas. Underlying this nonsmooth and level-resolved dynamics is a simple equality about the sinc function \sinc x \equiv \sin x / x. These physical effects appear in many systems with approximately equally spaced spectra, and is also robust for larger-amplitude coupling beyond the domain of perturbation theory. We use a one-dimensional periodically driven tight-binding model to illustrate these effects, both within and outside the perturbative regime.Comment: Link with the Paley-Wiener theorem and another reference is added; any comment is welcome and will be greatly appreciated

    PPM1D phosphatase, a target of p53 and RBM38 RNA-binding protein, inhibits p53 mRNA translation via dephosphorylation of RBM38.

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    PPM1D phosphatase, also called wild-type p53-induced phosphatase 1, promotes tumor development by inactivating the p53 tumor suppressor pathway. RBM38 RNA-binding protein, also called RNPC1 and a target of p53, inhibits p53 messenger RNA (mRNA) translation, which can be reversed by GSK3 protein kinase via phosphorylation of RBM38 at serine 195. Here we showed that ectopic expression of RBM38 increases, whereas knockdown of RBM38 inhibits, PPM1D mRNA translation. Consistent with this, we found that RBM38 directly binds to PPM1D 3'-untranslated region (3'-UTR) and promotes expression of a heterologous reporter gene that carries PPM1D 3'-UTR in a dose-dependent manner. Interestingly, we showed that PPM1D directly interacts with and dephosphorylates RBM38 at serine 195. Furthermore, we showed that PPM1D modulates p53 mRNA translation and p53-dependent growth suppression through dephosphorylation of RBM38. These findings provide evidence that the crosstalk between PPM1D and RBM38, both of which are targets and modulators of p53, has a critical role in p53 expression and activity

    Witnessing a Poincar\'e recurrence with Mathematica

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    The often elusive Poincar\'e recurrence can be witnessed in a completely separable system. For such systems, the problem of recurrence reduces to the classic mathematical problem of simultaneous Diophantine approximation of multiple numbers. The latter problem then can be somewhat satisfactorily solved by using the famous Lenstra-Lenstra-Lov\'{a}sz (LLL) algorithm, which is implemented in the Mathematica built-in function \verb"LatticeReduce". The procedure is illustrated with a harmonic chain. The incredibly large recurrence times are obtained exactly. They follow the expected scaling law very well.Comment: 8 pages, 5 figure

    Exotic Hill Problem: Hall motions and symmetries

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    Our previous study of a system of bodies assumed to move along almost circular orbits around a central mass, approximately described by Hill's equations, is extended to "exotic" [alias non-commutative] particles. For a certain critical value of the angular velocity, the only allowed motions follow the Hall law. Translations and generalized boosts span two independent Heisenberg algebras with different central parameters. In the critical case, the symmetry reduces to a single Heisenberg algebra.Comment: RevTeX, 4 pages, 4 figure