The finite volume method based on stabilized finite element for the stationary Navier–Stokes problem

AbstractA finite volume method based on stabilized finite element for the two-dimensional stationary Navier–Stokes equations is investigated in this work. A macroelement condition is introduced for constructing the local stabilized formulation for the problem. We obtain the well-posedness of the FVM based on stabilized finite element for the stationary Navier–Stokes equations. Moreover, for quadrilateral and triangular partition, the optimal H1 error estimate of the finite volume solution uh and L2 error estimate for ph are introduced. Finally, we provide a numerical example to confirm the efficiency of the FVM

MCTS-GEB: Monte Carlo Tree Search is a Good E-graph Builder

Rewrite systems [6, 10, 12] have been widely employing equality saturation [9], which is an optimisation methodology that uses a saturated e-graph to represent all possible sequences of rewrite simultaneously, and then extracts the optimal one. As such, optimal results can be achieved by avoiding the phase-ordering problem. However, we observe that when the e-graph is not saturated, it cannot represent all possible rewrite opportunities and therefore the phase-ordering problem is re-introduced during the construction phase of the e-graph. To address this problem, we propose MCTS-GEB, a domain-general rewrite system that applies reinforcement learning (RL) to e-graph construction. At its core, MCTS-GEB uses a Monte Carlo Tree Search (MCTS) [3] to efficiently plan for the optimal e-graph construction, and therefore it can effectively eliminate the phase-ordering problem at the construction phase and achieve better performance within a reasonable time. Evaluation in two different domains shows MCTS-GEB can outperform the state-of-the-art rewrite systems by up to 49x, while the optimisation can generally take less than an hour, indicating MCTS-GEB is a promising building block for the future generation of rewrite systems

Formation and Destiny of White Dwarf and Be Star Binaries

The binary systems consisting of a Be star and a white dwarf (BeWDs) are very interesting.They can originate from the binaries composed of a Be star and a subdwarf O or B star (BesdOBs), and they can merge into red giants via luminous red nova or can evolve into double WD potentially detected by $LISA$ mission. Using the method of population synthesis, we investigate the formation and the destiny of BeWDs,and discuss the effects of the metallicity ($Z$) and the common envelope evolution parameters. We find that BesdOBs are significant progenitors of BeWDs. About 30\% ($Z=0.0001$)-50\% ($Z=0.02$) of BeWDs come from BesdOBs. About 60\% ($Z=0.0001$) -70\% ($Z=0.02$) of BeWDs turn into red giants via a merger between a WD and a non-degenerated star. About 30\% ($Z=0.0001$) -40\% ($Z=0.02$) of BeWDs evolve into double WDs which are potential gravitational waves of $LISA$ mission at a frequency band between about $3\times10^{-3}$ and $3\times10^{-2}$ Hz. The common envelope evolution parameter introduces an uncertainty with a factor of about 1.3 on BeWD populations in our simulations.Comment: 17 pages, 12 figures, 2 table, accepted for publication in RA

Delay-dependent stabilization of stochastic interval delay systems with nonlinear disturbances

This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2007 Elsevier Ltd.In this paper, a delay-dependent approach is developed to deal with the robust stabilization problem for a class of stochastic time-delay interval systems with nonlinear disturbances. The system matrices are assumed to be uncertain within given intervals, the time delays appear in both the system states and the nonlinear disturbances, and the stochastic perturbation is in the form of a Brownian motion. The purpose of the addressed stochastic stabilization problem is to design a memoryless state feedback controller such that, for all admissible interval uncertainties and nonlinear disturbances, the closed-loop system is asymptotically stable in the mean square, where the stability criteria are dependent on the length of the time delay and therefore less conservative. By using Itô's differential formula and the Lyapunov stability theory, sufficient conditions are first derived for ensuring the stability of the stochastic interval delay systems. Then, the controller gain is characterized in terms of the solution to a delay-dependent linear matrix inequality (LMI), which can be easily solved by using available software packages. A numerical example is exploited to demonstrate the effectiveness of the proposed design procedure.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Nuffield Foundation of the UK under Grant NAL/00630/G, and the Alexander von Humboldt Foundation of Germany

First Detailed Analysis of a Relatively Deep, Low Mass-ratio Contact Binary: ATO J108.6991+27.8306

We present the first detailed photometric analysis of ATO J108.6991+27.8306 (hereinafter as J108). The short-period close binary J108 was observed by the Nanshan 1 m Wide Field Telescope of the Xinjiang Astronomical Observatory. The obtained BVRI-band light curves were used to determine the photometric solution by using the 2003 version of the Wilson-Devinney code. J108 is a typical deep ( f > 50%), low mass ratio (q < 0.25) overcontact binary system with a mass ratio of q = 0.1501 and a fill-out factor of f = 50.1 %, suggesting that it is in the late evolutionary stage of contact binary systems. We found the target to be a W-type W UMa binary and provided evidence for the presence of starspots on both components. From the temperature-luminosity diagram, the main component is the evolved main sequence star with an evolutionary age of about 7.94 Gyr.Comment: 7 pages, 6 figure

A New Soliton Hierarchy Associated with so

Based on the three-dimensional real special orthogonal Lie algebra so(3,R), we construct a new hierarchy of soliton equations by zero curvature equations and show that each equation in the resulting hierarchy has a bi-Hamiltonian structure and thus integrable in the Liouville sense. Furthermore, we present the infinitely many conservation laws for the new soliton hierarchy

Asymptotic Soft Filter Pruning for Deep Convolutional Neural Networks

Deeper and wider Convolutional Neural Networks (CNNs) achieve superior performance but bring expensive computation cost. Accelerating such over-parameterized neural network has received increased attention. A typical pruning algorithm is a three-stage pipeline, i.e., training, pruning, and retraining. Prevailing approaches fix the pruned filters to zero during retraining, and thus significantly reduce the optimization space. Besides, they directly prune a large number of filters at first, which would cause unrecoverable information loss. To solve these problems, we propose an Asymptotic Soft Filter Pruning (ASFP) method to accelerate the inference procedure of the deep neural networks. First, we update the pruned filters during the retraining stage. As a result, the optimization space of the pruned model would not be reduced but be the same as that of the original model. In this way, the model has enough capacity to learn from the training data. Second, we prune the network asymptotically. We prune few filters at first and asymptotically prune more filters during the training procedure. With asymptotic pruning, the information of the training set would be gradually concentrated in the remaining filters, so the subsequent training and pruning process would be stable. Experiments show the effectiveness of our ASFP on image classification benchmarks. Notably, on ILSVRC-2012, our ASFP reduces more than 40% FLOPs on ResNet-50 with only 0.14% top-5 accuracy degradation, which is higher than the soft filter pruning (SFP) by 8%.Comment: Extended Journal Version of arXiv:1808.0686