Adult bones are continuously remodeled by the balance between bone resorption by osteoclasts and subsequent bone formation by osteoblasts. Many studies have provided molecular evidence that bone remodeling is under the control of circadian rhythms. Circadian fluctuations have been reported in the serum and urine levels of bone turnover markers, such as digested collagen fragments and bone alkaline phosphatase. Additionally, the expressions of over a quarter of all transcripts in bones show circadian rhythmicity, including the genes encoding master transcription factors for osteoblastogenesis and osteoclastogenesis, osteogenic cytokines, and signaling pathway proteins. Serum levels of calcium, phosphate, parathyroid hormone, and calcitonin also display circadian rhythmicity. Finally, osteoblast- and osteoclast-specific knockout mice targeting the core circadian regulator gene Bmal1 show disrupted bone remodeling, although the results have not always been consistent. Despite these studies, however, establishing a direct link between circadian rhythms and bone remodeling in vivo remains a major challenge. It is nearly impossible to repeatedly collect bone materials from human subjects while following circadian changes. In addition, the differences in circadian gene regulation between diurnal humans and nocturnal mice, the main model organism, remain unclear. Filling the knowledge gap in the circadian regulation of bone remodeling could reveal novel regulatory mechanisms underlying many bone disorders including osteoporosis, genetic diseases, and fracture healing. This is also an important question for the basic understanding of how cell differentiation progresses under the influence of cyclically fluctuating environments.
We introduce and study translation numbers for automorphisms of principal $\mathbb{Z}$-bundles and flat principal $\mathbb{R}$-bundles. We use them to show a vanishing result of a characteristic class of foliated bundles and to detect undistortion elements in the group of bundle automorphisms.
We provide sufficient conditions on integrable analytic Hamiltonians that guarantee the existence, under arbitrary sufficiently small analytic perturbations, of invariant lower dimensional tori associated to an invariant resonant torus of the unperturbed Hamiltonian.
For a relative equilibrium of a symmetric simple mechanical system, if the Morse index of the corresponding amended potential is odd, whether the nullity is zero or not, it is linearly unstable. We also provide a sufficient condition for spectral instability.
In this paper, we prove a reducibility result for a relativistic Schrödinger equation on torus with time quasi-periodic unbounded perturbations of order 1/2, and finally conjugate the original equation to a time independent, 2\times 2 block diagonal one.
We consider polygonal billiards and we show the uniqueness of coding of non-periodic billiard trajectories in polygons whose holes have non-zero minimal diameters, generalising a theorem of Galperin, Krüger and Troubetzkoy.
The set of directions from a quadratic differential that diverge on average under Teichmuller geodesic flow has Hausdorff dimension exactly equal to one-half.
Fully oscillating sequences are orthogonal to all topological dynamical systems of quasi-discrete spectrum in the sense of Hahn-Parry. This orthogonality concerns with not only simple but also multiple ergodic means. It is stronger than that required by Sarnak's conjecture.
We prove that the topological entropy of real unimodal maps depends as a Hoelder continuous function of the kneading parameter, and the local Hoelder exponent equals, up to a factor log 2, the value of the function at that point.
We prove the local mixing theorem for geodesic flows on abelian covers finite volume hyperbolic surfaces with cusps, which is a continuation of the work of Oh-Pan. We also describe applications to counting problems and the prime geodesic theorem.
We consider time-periodic patterns of the dissipative three dimensional baroclinic quasigeostrophic model in spherical coordinates, under time-dependent forcing. We show that when the forcing is time-periodic and the spatial square-integral of the forcing is bounded in time, the model has time-periodic solutions.
We show that the Feigenbaum-Cvitanovic equation can be interpreted as a linearizing equation, and the domain of analyticity of the Feigenbaum fixed point of renormalization as a basin of attraction. There is a natural decomposition of this basin which enables to recover a result of local connectivity by Jiang and Hu for the Feigenbaum Julia set.
We prove that natural generating functions for enumeration of branched coverings of the pillowcase orbifold are level 2 quasimodular forms. This gives a way to compute the volumes of the strata of the moduli space of quadratic differentials.
We give a geometric criterion that guaranteesa purely singular spectral type for a dynamical system on a Riemannian manifold. The criterion, that is based on the existence of fairly rich but localized periodic approximations, is compatible with mixing. Indeed, we use it to construct examples of smooth mixing flows on the three torus with purely singular spectra.
We investigate a class of area preserving non-uniformly hyperbolic maps of the two torus. First we establish some results on the regularity of the invariant foliations, then we use this knowledge to estimate the rate of mixing.
Given a new definition for the entropy of a cellular automata acting on a two-dimensional space, we propose an inequality between the entropy of the shift on a two-dimensional lattice and some angular analog of Lyapunov exponents.