SOX4 facilitates PGR protein stability and FOXO1 expression conducive for human endometrial decidualization

The establishment of receptive endometrium in human necessitates appropriate decidualization of stromal cells, which involves steroids regulated periodic transformation of endometrial stromal cells during menstrual cycle. Insufficient decidualization of endometrium contributes to not only the failure of embryo implantation and unexplained infertility, but also the occurrence of recurrent spontaneous abortion, intrauterine growth retardation, preeclampsia, and other clinical gynecological diseases. However, the potential molecular regulatory mechanism underlying the initiation and maintenance of decidualization in humans is yet to be fully elucidated. In this investigation, we document that SOX4 is a key regulator of human endometrial stromal cells (hESCs) decidualization by directly regulating PRL and FOXO1 expression as revealed by whole genomic binding of SOX4 assay and RNA-Seq. Besides, our immunoprecipitation and mass spectrometry results unravel that SOX4 modulates progesterone receptor (PGR) stability through repressing E3 ubiquitin ligase HERC4 mediated degradation. More importantly, we provide evidence that dysregulated SOX4-HERC4-PGR axis is a potential cause of defective decidualization and recurrent implantation failure (RIF) in IVF patients. In summary, this study evidences that SOX4 is a new and critical regulator for human endometrial decidualization, and provides insightful information for the pathology of decidualization-related infertility and will pave the way for pregnancy improvement.

A dual weighted residual method applied to complex periodic gratings

An extension of the dual weighted residual (DWR) method to the analysis of electromagnetic waves in a periodic diffraction grating is presented. Using the α ,0-quasi-periodic transformation, an upper bound for the a posteriori error estimate is derived. This is then used to solve adaptively the associated Helmholtz problem. The goal is to achieve an acceptable accuracy in the computed diffraction efficiency while keeping the computational mesh relatively coarse. Numerical results are presented to illustrate the advantage of using DWR over the global a posteriori error estimate approach. The application of the method in biomimetic, to address the complex diffraction geometry of the Morpho butterfly wing is also discussed.

Reducibility for a Class of Almost-Periodic Differential Equations with Degenerate Equilibrium Point under Small Almost-Periodic Perturbations

This paper focuses on almost-periodic time-dependent perturbations of an almost-periodic differential equation near the degenerate equilibrium point. Using the KAM method, the perturbed equation can be reduced to a suitable normal form with zero as equilibrium point by an affine almost-periodic transformation. Hence, for the equation we can obtain a small almost-periodic solution.

The Collocation Method and the Splitting Extrapolation for the First Kind of Boundary Integral Equations on Polygonal Regions

In this paper, the collocation methods are used to solve the boundary integral equations of the first kind on the polygon. By means of Sidi’s periodic transformation and domain decomposition, the errors are proved to possess the multi-parameter asymptotic expansion at the interior point with the powers (i = 1,...,d), which means that the approximations of higher accuracy and a posteriori estimation of the errors can be obtained by splitting extrapolations. Numerical experiments are carried out to show that the methods are very efficient.

Parallel implementation of an upwind Euler solver for hovering rotor flows

An Euler method for computing compressible hovering rotor flows is described. The equations are solved using an upwind finite-volume method in a blade-fixed rotating co-ordinate system, so that hover is a steady problem. Transfinite interpolation, along with a periodic transformation, is used to generate grids for the periodic domain. Computation of these flows to an acceptable accuracy requires fine grids, and a long integration time for the wake to develop, resulting in excessive run times on a single processor. Hence, the method is developed as a multiblock code in a parallel environment, and various aspects of data passing and communication between processors have been considered. It is shown that a considerable increase in performance is available from the use of non-blocking and asynchronous communication. It is also demonstrated that increased performance may be available by balancing the residual levels rather than the number of cells on each processor.

Infinitely Periodic Knots

One aspect of the study of 3-manifolds is to determine what finite group actions a given manifold has. Some important questions that one can ask about these actions on a given manifold are: What periods could they have? and, what sets of points may be fixed by the action? In the case of periodic transformations of homology spheres, Smith [18] classified the types of fixed point sets which could occur. For homology 3-spheres the fixed point set will be ∅, S0, S1, or S2. Fox [4] looked at periodic transformations of the three sphere which leave a knot invariant and, using Smith's classification of fixed point sets, determined that there were eight types of transformations according to how the fixed point set met the knot. For convenience we shall say a knot is (a, b)-periodic if there is a periodic transformation of S3 leaving the knot invariant with fixed point set homeomorphic to a and with the fixed point set meeting the knot in a set homeomorphic to b.