关键词： RANS modelling   Machine-learning   Evolutionary algorithm   Gene expression programming   Algebraic stress modelling  

摘要： This work presents developments to a novel evolutionary framework that symbolically regresses algebraic forms of the Reynolds stress anisotropy tensor. This work contributes to the growing trend in machine-learning for modelling physical phenomena. Our framework is shown to be computational inexpensive and produce accurate and robust models that are tangible mathematical expressions. This transparency in the result allows us to diagnose issues with the regressed formulae and appropriately make amendments, as we further understand the regression tools. Such models are created using hybrid RANS/LES flow field data and a passive solving of the RANS transport equations to obtain the modelled time scale. This process shows that models can be regressed from a qualitatively correct flow field and fully resolved DNS is not necessarily required. Models are trained and tested using rectangular ducts, an example flow genus that linear RANS models even qualitatively fail to predict correctly. A priori and a posteriori testing of the new models show that the framework is a viable methodology for RANS closure development. This a posteriori agenda includes testing on an asymmetric diffuser, for which the new models vastly outperform the baseline linear model. Therefore this study presents one of the most rigorous and complete CFD validation of machine learnt turbulent stress models to date.

关键词： SART algorithm   fast total variation   regularization   PET   image reconstruction  

摘要： Context: There has been considerable progress in the instrumentation for data measurement and computer methods for generating images of measured PET data. These computer methods have been developed to solve the inverse problem, also known as the "image reconstruction from projections'' problem. Aim: In this paper, we propose a modified Simultaneous Algebraic Reconstruction Technique (SART) algorithm to improve the quality of image reconstruction by incorporating total variation (TV) minimization into the iterative SART algorithm. Methodology: The SART updates the estimated image by forward projecting the initial image onto the sinogram space. Then, the difference between the estimated sinogram and the given sinogram is back-projected onto the image domain. This difference is then subtracted from the initial image to obtain a corrected image. Fast total variation (FTV) minimization is applied to the image obtained in the SART step. The second step is the result obtained from the previous FTV update. The SART and the FTV minimization steps run iteratively in an alternating manner. Fifty iterations were applied to the SART algorithm used in each of the regularization-basedmethods. In addition to the conventional SART algorithm, spatial smoothing was used to enhance the quality of the image. All images were sized at 128 x 128 pixels. Results: The proposed algorithm successfully accomplished edge preservation. A detailed scrutiny revealed that the reconstruction algorithms differed;for example, the SART and the proposed FTV-SART algorithm effectively preserved the hot lesion edges, whereas artifacts and deviations were more likely to occur in the ART algorithm than in the other algorithms. Conclusions: Compared to the standard SART, the proposed algorithm is more robust in removing background noise while preserving edges to suppress the existent image artifacts. The quality measurements and visual inspections show a significant improvement in image quality compared to th

关键词： 高中数学   算法教学   问题   对策  

摘要： 高中算法教学是新课标对高中数学教学提出的最新教学内容,适应了现阶段信息技术高速发展的社会需要,为此,高中数学教师在教学中应该充分认识到算法在现代社会中的重要价值,通过不断改善教学方法和创新教学理念,解决在算法教学中存在的诸多问题,不断提高高中数学算法教学的质量。

关键词： 算法设计   算法思想   教学渗透  

摘要： 本文首先对算法的含义与算法思想进行了介绍,算法具有广泛的应用价值,有着深远的历史渊源。再讲述了算法教育在当代显得尤为重要,有很大的意义。同时,算法进入中学数学课程,反映了时代的要求。教学中应逐步渗透算法思想。

关键词： 高中数学   新课程   算法思想   应用分析  

摘要： 算法已成为高中数学新课程的必修内容,对于中学数学教育来说是一个全新的课题。算法的含义是解决问题的程序和步骤,它具有有穷性、确定性、可行性、通用性等特征,由于算法的抽象性,很多学生在学习起来感到困难重重。本文将对高中数学算法思想的重要性进行论述,分析和探讨新课程环境背景下高中数学教学中算法思想的应用策略。

关键词： 网格多边形   数学核心素养   问题解决   理性思维  

摘要： 原创一道网格背景下多种算法解决多边形面积的题目，可以有助于培养学生的数学核心素养。具体而言，可以通过以下路径展开：研发学习素材，为学生创设研究问题的空间；鼓励独立思考，培养科学精神；在个性化解法的生成中，培养学生勇于探索的精神；在算法多样化的交流中培养学生理性思维；在活动经验的积累中，培养学生批判质疑的精神。特别是当学生遇到看似无法解决的问题时，鼓励学生探索问题解决的新途径，培养学生反思问题的解决过程，从而更好地感悟学习方法。

关键词： 数学形态学   匹配追踪   去噪  

摘要： 脉搏信号属于一种非线性非平稳的生理信号,是临床诊断和医学研究的重要参考依据。针对其采集时易受外界噪声干扰的问题,提出了一种基于数学形态学滤波和MP算法的去噪方法。先利用数学形态滤波法滤除包含的随机分布的白噪声,然后再引入MP算法消除含有的基线漂移,从而得到去噪后的脉搏信号。仿真结果表明,与单一的去噪方法相比,该方法能够更加有效地去除脉搏信号中的白噪声和基线漂移。

关键词： algebraic eigenvalue problem   computer of hybrid architecture   hybrid algorithm   subspace iteration method   conjugate gradient methods   efficiency of parallel algorithms  

摘要： Hybrid algorithms for solving the partial generalized eigenvalue problem for symmetric positive definite sparse matrices of different structures by hybrid computers with graphic processors are proposed, coefficients for the efficiency of the algorithms are obtained, and approbation of the developed algorithms for test and practical problems is carried out.

关键词： Bayesian image reconstruction   deconvolution   nonsmooth convex optimization   partial differential equations (PDEs)   preconditioning   quantitative susceptibility mapping (QSM)  

摘要： Quantitative susceptibility mapping (QSM) solves the magnetic field-to-magnetization (tissue susceptibility) inverse problem under conditions of noisy and incomplete field data acquired using magnetic resonance imaging. Therefore, sophisticated algorithms are necessary to treat the ill-posed nature of the problem and are reviewed here. The forward problem is typically presented as an integral form, where the field is the convolution of the dipole kernel and tissue susceptibility distribution. This integral form can be equivalently written as a partial differential equation (PDE). Algorithmic challenges are to reduce streaking and shadow artifacts characterized by the fundamental solution of the PDE. Bayesian maximum a posteriori estimation can be employed to solve the inverse problem, where morphological and relevant biomedical knowledge (specific to the imaging situation) are used as priors. As the cost functions in Bayesian QSM framework are typically convex, solutions can be robustly computed using a gradient-based optimization algorithm. Moreover, one can not only accelerate Bayesian QSM, but also increase its effectiveness at reducing shadows using prior knowledge based preconditioners. Improving the efficiency of QSM is under active development, and a rigorous analysis of preconditioning needs to be carried out for further investigation.

关键词： Algebraic velocity estimation   estimation system   nonlinear servomechanism   on-line parameter identification   persistent excitation   real-time experiments  

摘要： This paper presents a methodology for on-line closed-loop identification of a class of nonlinear servomechanisms. First, a system is defined with the same structure as the actual servomechanism, but using time-varying estimated parameters. No coupling between the actual and the estimation systems is present. Position, velocity and acceleration errors, defined as the difference of the actual respective signals and the signals coming from the estimation system, are required in the identification method. Then, a recursive algorithm for on-line identification of the system parameters is derived from a cost function depending on a linear combination of all the estimation errors. Velocity and acceleration estimates, required in the proposed parameter identification algorithm, are obtained by using an algebraic methodology. The identification algorithm is compared by means of real-time experiments with an on-line least squares algorithm with forgetting factor and an off-line least squares algorithm with data preprocessing. Experimental results show that the proposed approach has a performance comparable to that obtained with the off-line least squares algorithm, but with the advantage of avoiding any preprocessing.