A p-ADAPTIVE LOCAL DISCONTINUOUS GALERKIN LEVEL SET METHOD FOR WILLMORE FLOW

International audienceThe level set method is often used to capture interface behavior in two or three dimensions. In this paper, we present a combination of local discontinuous Galerkin (LDG) method and level set method for simulating Willmore flow. The LDG scheme is energy stable and mass conservative, which are good properties comparing with other numerical methods. In addition, to enhance the efficiency of the proposed LDG scheme and level set method, we employ a p-adaptive local discontinuous Galerkin technique, which applies high order polynomial approximations around the zero level set and low order ones away from the zero level set. A major advantage of the level set method is that the topological changes are well defined and easily performed. In particular, given the stiffness of Willmore flow, a high order semi-implicit Runge-Kutta method is employed for time discretization, which allows larger time step. The equations at the implicit time level are linear, we demonstrate an efficient and practical multi-grid solver to solve the equations. Numerical examples are given to illustrate the combination of the LDG scheme and level set method provides an efficient and practical approach when simulating the Willmore flow

Large-Scale Public Data Improves Differentially Private Image Generation Quality

Public data has been frequently used to improve the privacy-accuracy trade-off of differentially private machine learning, but prior work largely assumes that this data come from the same distribution as the private. In this work, we look at how to use generic large-scale public data to improve the quality of differentially private image generation in Generative Adversarial Networks (GANs), and provide an improved method that uses public data effectively. Our method works under the assumption that the support of the public data distribution contains the support of the private; an example of this is when the public data come from a general-purpose internet-scale image source, while the private data consist of images of a specific type. Detailed evaluations show that our method achieves SOTA in terms of FID score and other metrics compared with existing methods that use public data, and can generate high-quality, photo-realistic images in a differentially private manner

Efficient high order semi-implicit time discretization and local discontinuous Galerkin methods for highly nonlinear PDEs

International audienceIn this paper, we develop a high order semi-implicit time discretization method for highly nonlinear PDEs, which consist of the surface diffusion and Willmore flow of graphs, the Cahn-Hilliard equation and the Allen-Cahn/Cahn-Hilliard system. These PDEs are high order in spatial derivatives, which motivates us to develop implicit or semi-implicit time marching methods to relax the severe time step restriction for stability of explicit methods. In addition, these PDEs are also highly nonlinear, fully implicit method will incredibly increase the difficulty of implementation. In particular, we can not well separate the stiff and non-stiff components for these problems, which leads to the traditional implicit-explicit methods nearly meaningless. In this paper, a high order semi-implicit time marching method and the local discontinuous Galerkin spatial method are coupled together to achieve high order accuracy in both space and time, and to enhance the efficiency of the proposed approaches, the resulting linear or nonlinear algebraic systems are solved by multigrid solver. Numerical simulation results in one and two dimensions are presented to illustrate that the combination of the local discontinuous Galerkin method for spatial approximation, semi-implicit temporal integration with the multigrid solver provides a practical and efficient approach when solving this family of problems

Large shift current, π\pi Zak phase and unconventional nature in Se and Te

Recently, unconventional materials (or obstructed atomic insulators) have attracted lots of attention owing to the unconventional feature of mismatch between Wannier centers and atomic positions. In this paper, we demonstrate that the trigonal Selenium and Tellurium host unconventional nature in both electronic and phonon spectra. In electronic band structures, the band representation (BR) decomposition for occupied bands has to contain the essential BR of $A@3b$, and the real-space invariant is $\delta_1@3b=-1$. The unconventional nature is related to the $\pi$ Zak phase, suggesting that the one-dimensional Se/Te chain is a chiral Su-Schrieffer-Heeger (SSH) chain. The effective magnetism can be induced by $p$ states at ends. More importantly, a large shift current is obtained in Se quantum well, making it a good candidate for the utilization of solar energy via bulk photovoltaic effect. In addtion, in phonon spectra, three sets of phonon bands are well separated and assigned to $B@3b$, $B@3a$, and $A@3b$ BRs, respectively. Thus, the obstructed phonon states are predicted on the (0001)-surface phonon spectrum. As the prototypes of unconventional materials in both electronic and phonon spectra, our findings could intrigue much interest on the study of obstructed surface electronic and phonon states in this kind of novel materials

LH level on the antagonist administration day as a predictor of the reproductive outcomes in women with normal ovarian function

IntroductionThe addition of antagonists is mainly based on estrogen level and follicle size, while LH level has not received sufficient attention.In this study, LH Level on the antagonist administration day was used as the main research objective to explore its relationship with laboratory indicators and pregnancy outcomes.Methods and AnalysisWe enrolled 854 patients with normal ovarian function undergoing in-vitro fertilization (IVF) or intracytoplasmic sperm injection (ICSI) between May 2021 to May 2022 at the Reproductive Center of Shandong University of Traditional Chinese Medicine.We used the quartile method to group LH levels on the antagonist administration day. There were four groups: Q1 (0.53IU/L≤LH ≤ 1.89IU/L); Q2 (1.89IU/L<LH ≤ 3.01IU/L); Q3 (3.01IU/L<LH≤ 5.29 IU/L); Q4 (5.29IU/L<LH ≤ 8.72IU/L). A total of 452 fresh embryo transplantation cycles and 1726 Frozen embryo transplantation cycles were carried out.ResultThere were significant differences among the four groups in terms of total Gn dosage, E2, P and LH on trigger day, number of retrieved oocytes, number of 2PN embryos, number of blastocysts, Number of ET and fresh ETR.There is a significant correlation between LH on antagonist administration day and Basal LH Level,LH on trigger day,number of oocytes retrieved,number of 2PN embryos,number of blastocysts, number of ET.Using Fresh ETR,Fresh CPR,OHSS and Cumulative CPR as the criterion respectively, the optimal cut-off value for evaluating LH on antagonist administration day was 4.18IU/L,3.99IU/L,4.63IU/L,4.66IU/L.ConclusionThere was a significant positive correlation between LH on the antagonist administration day and number of oocytes retrieved,number of 2PN embryos,number of blastocysts.LH on the antagonist administration day could predict Fresh CPR,OHSS and Cumulative CPR to some extent

Local Discontinuous Galerkin Methods for the Functionalized Cahn–Hilliard Equation

© 2014, Springer Science+Business Media New York. In this paper, we develop a local discontinuous Galerkin (LDG) method for the sixth order nonlinear functionalized Cahn–Hilliard (FCH) equation. We address the accuracy and stability issues from simulating high order stiff equations in phase-field modeling. Within the LDG framework, various boundary conditions associated with the background physics can be naturally implemented. We prove the energy stability of the LDG method for the general nonlinear case. A semi-implicit time marching method is applied to remove the severe time step restriction (Δt∼O(Δx6)) for explicit methods. The h-p adaptive capability of the LDG method allows for capturing the interfacial layers and the complicated geometric structures of the solution with high resolution. To enhance the efficiency of the proposed approach, the multigrid (MG) method is used to solve the system of linear equations resulting from the semi-implicit temporal integration at each time step. We show numerically that the MG solver has mesh-independent convergence rates. Numerical simulation results for the FCH equation in two and three dimensions are provided to illustrate that the combination of the LDG method for spatial approximation, semi-implicit temporal integration with the MG solver provides a practical and efficient approach when solving this family of problems