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1. chinaXiv:201910.00071 [pdf]

Sparse Representation Based Efficient Radiation Symmetry Analysis Method for Cylindrical Model of Inertial Confinement Fusion

张雁峰
Subjects: Mathematics >> Modeling and Simulation

Radiation symmetry evaluation is critical to the laser driven Inertial Confinement Fusion (ICF), which is usually done by solving a view-factor equation model. The model is nonlinear, and the number of equations can be very large when the size of discrete mesh element is very small to achieve a prescribed accuracy, which may lead to an intensive equation solving process. In this paper, an efficient radiation symmetry analysis approach based on sparse representation is presented, in which, 1) the Spherical harmonics, annular Zernike polynomials and Legendre-Fourier polynomials are employed to sparsely represent the radiation flux on the capsule and cylindrical cavity, and the nonlinear energy equilibrium equations are transformed into the equations with sparse coefficients, which means there are many redundant equations, 2) only a few equations are selected to recover such sparse coefficients with Latin hypercube sampling, 3) a Conjugate Gradient Subspace Thresholding Pursuit (CGSTP) algorithm is then given to rapidly obtain such sparse coefficients equation with as few iterations as possible. Finally, the proposed method is validated with two experiment targets for Shenguang II and Shenguang III laser facility in China. The results show that only one tenth of computation time is required to solve one tenth of equations to achieve the radiation flux with comparable accuracy. Further more, the solution is much more efficient as the size of discrete mesh element decreases, in which, only 1.2% computation time is required to obtain the accurate result.

submitted time 2019-10-23 Hits1190Downloads22 Comment 0

2. chinaXiv:201910.00074 [pdf]

基于线性模型平均估计的置信区间

王苗苗
Subjects: Mathematics >> Statistics and Probability

已有的关于模型平均估计渐近分布理论的研究多是基于局部误设定的假设,[1] 是其中开创性的且最著名的文章之一. 虽然利用局部误设定的假设可以证明模型平均估计渐近分布理论, 但是 [2] 等对此假设提出了不合理性质疑和解释. 本文我们研究[1]中的置信区间估计方法. 证明了在一般参数设定下, 虽然 [1]中的渐近分布理论不一定成立, 但是关于不确定参数的线性函数的置信区间在正态分布误差、线性回归模 型下是有效的, 即置信区间的覆盖率趋于预设定的名义水平. 我们通过模拟研究进一步验证了理论结果.

submitted time 2019-10-14 Hits643Downloads28 Comment 0

3. chinaXiv:201909.00015 [pdf]

Analytical expressions of copositivity for 4th order symmetric tensors and applications

宋义生; 祁力群
Subjects: Mathematics >> Control and Optimization.

In particle physics, scalar potentials have to be bounded from below in order for the physics to make sense. The precise expressions of checking lower bound of scalar potentials are essential, which is an analytical expression of checking copositivity and positive definiteness of tensors given by such scalar potentials. Because the tensors given by general scalar potential are 4th order and symmetric, our work mainly focuses on finding precise expressions to test copositivity and positive definiteness of 4th order tensors in this paper. First of all, an analytically sufficient and necessary condition of positive definiteness is provided for 4th order 2 dimensional symmetric tensors. For 4th order 3 dimensional symmetric tensors, we give two analytically sufficient conditions of (strictly) cpositivity by using proof technique of reducing orders or dimensions of such a tensor. Furthermore, an analytically sufficient and necessary condition of copositivity is showed for 4th order 2 dimensional symmetric tensors. We also give several distinctly analytically sufficient conditions of (strict) copositivity for 4th order 2 dimensional symmetric tensors. Finally, we apply these results to check lower bound of scalar potentials, and to present analytical vacuum stability conditions for potentials of two real scalar fields and the Higgs boson.

submitted time 2019-08-30 Hits192Downloads90 Comment 0

4. chinaXiv:201908.00121 [pdf]

一中求解特征值问题的广义共轭梯度算法

谢和虎; 张宁; 李瑜; 徐然; 游春光
Subjects: Mathematics >> Computational Mathematics.

本文基于阻尼块反幂法与子空间投影算法设计了一种求解特征值问题的广义共轭梯度算法, 同时也实现了相应的计算软件包. 然后对算法和计算过程进行了一系列的优化来提高算法的稳定性、计算效率和并行可扩展性, 使得本文的算法适合在并行计算环境下求解大规模稀疏矩阵的特征值. 所形成的软件包是基于Matrix-Free和Vector-Free设计的, 可以应用于任意的矩阵向量结构. 针对几种典型矩阵的测试结果表明本文的算法和软件包不但具有良好的数值稳定性, 同时相比于SLEPc软件包中的LOBPCG以及Jacobi-Davidson解法器有2-6倍的效率提升. 软件包的网址: https://github.com/pase2017/GCGE-1.0.

submitted time 2019-08-27 Hits230Downloads113 Comment 0

5. chinaXiv:201705.00826 [pdf]

Relative Entropy Minimizing-Based Theory of Intelligent Systems

Xi, Guangcheng
Subjects: Mathematics >> Statistics and Probability

Based on the point of view of neuroethology and cognition-psychology, general frame of theory for intelligent systems is presented by means of principle of relative entropy minimizing in this paper. Cream of the general frame of theory is to present and to prove basic principle of intelligent systems: entropy increases or decreases together with intelligence in the intelligent systems. The basic principle is of momentous theoretical significance and practical significance .From the basic principle can not only derive two kind of learning algorithms (statistical simulating annealing algorithms and annealing algorithms of mean-field theory approximation) for training large kinds of stochastic neural networks,but also can thoroughly dispel misgivings created by second law of thermodynamics on 'peoplespsychology ,hence make one be fully confident of facing life.Because of Human society, natural world, and even universe all are intelligent systems.

submitted time 2019-07-21 Hits2332Downloads959 Comment 0

6. chinaXiv:201907.00015 [pdf]

一道工序智能加工系统 RGV 调度模型

周伟刚; 冯倩倩
Subjects: Mathematics >> Applied Mathematics

研究了一道工序智能加工系统轨道式自动引导车(RGV)调度问题. 该问题为2018年全国大学生数学建模竞赛B题的一部分. 系统由一辆轨道式自动引导车和若干台计算机数控机床(CNC)等部件组成, RGV操控多台CNC完成多个物料加工, RGV调度方案决定了系统的效率. 以 RGV的移动路径为决策变量, 以RGV在CNC上的操作结束时刻为时间节点, 以物料加工剩余时间为状态变量, 给出了问题的数学模型, 但模型中的部分参数以决策变量为下标. 通过定义新的变量和约束, 将模型修改为不含变量下标和分段函数的非线性混合整数规划模型. 最后给出了算例, 说明了模型的正确性和可操作性.

submitted time 2019-07-16 Hits2816Downloads172 Comment 0

7. chinaXiv:201904.00081 [pdf]

接圆回归

何沧平
Subjects: Mathematics >> Computational Mathematics.

本文提出一个名为接圆回归的点击率预测新方法,尝试替代常用的因子分解机(FM)。接圆回归用超平面拼接出一个封闭凸多面体,圈出正样本,有直观的几何解释, 能从任意初始值一次收敛到全局最优解。 拟合出来的曲面Lipschitz连续,变化平缓。在人工设计的星环集、双堆集、双月集上,接圆回归的分类准确性、解释性、平滑性全面超过FM。在同量级参数量、计算量 的条件下,接圆回归在Avazu集和Criteo集上的AUC超过FM。

submitted time 2019-04-10 Hits2035Downloads324 Comment 0

8. chinaXiv:201705.00829 [pdf]

Entropy-partition of Complex Systems and Emergence of Human Brain’s Consciousness

Xi Guangcheng
Subjects: Mathematics >> Statistics and Probability

The three frameworks for theories of consciousness taken moust seriously by neuroscientists are that consciousness is a biological state of the brain,the global workspace perspective,and the perspective of higher state. Consciousness is discussed from viewpoint of theory of Entropy—partition of complex system in present article. Human brain’s system self-organizably and adaptively implements partition、aggregation and integration, and consciousness emerges.

submitted time 2019-01-10 Hits2173Downloads1123 Comment 0

9. chinaXiv:201803.01556 [pdf]

Gibbsian representation of knowledge in infinite dimensional random neural networks(IDRNN)

xi guangcheng
Subjects: Mathematics >> Statistics and Probability

Abstract. In studying of a class of random neural network, some of relative researchers have proposed Markov model of neural network. Wherein Markov property of the neural network is based on “assuming”. To reveal mechanism of generating of Markov property in neural network, it is studied how infinite-dimensional random neural network (IDRNN) forms inner Markov representation of environment information in this paper.Because of equivalence between markov property and Gibbsian our conclusion is that knowledge is eventually expressed by extreme Gibbs probability measure—ergodic Gibbs probability measure in IDRNN. This conclusion is also applicable to quantum mechanical level of IDRNN. Hence one can see “ concept “- “ consciousness” is generated at particle(ion) level in the brain and is experienced at the level of the neurons; We have discussed also ergodicity of IDRNN with random neural potential.

submitted time 2018-11-07 Hits1609Downloads729 Comment 0

10. chinaXiv:201810.00001 [pdf]

霍奇星算子与外微分算符的组合规律

彭俊金
Subjects: Physics >> The Physics of Elementary Particles and Fields

本文系统地探讨了霍奇星算子与外微分算符作用于任意微分形式场时两者的一般组合规律。首先,找到了保持微分形式场的次不变的两个组合算符,并通过二者的线性组合得到了一个新算符。其次,当由任意数目的霍奇星算子与外微分算符进行组合时,作者导出了所有形式上彼此互异的组合算符的统一表达式,这些表达式由单个霍奇星算子与外微分算符以及二者的任选两个的非零组合构成。在此基础上,分析了所有算符之间的相互作用关系,并根据这些算符对微分形式的次的改变情况,对它们进行了具体分类。最后,作为一个应用,作者详细讨论了如何由次相同的微分形式的线性组合来构造电磁场的麦克斯韦方程。

submitted time 2018-10-08 Hits1855Downloads627 Comment 0

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