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1. chinaXiv:202105.00041 [pdf]

基于高阶AGO生成的GM(1,1)模型

倪嘉雨; 涂缘
Subjects: Mathematics >> Modeling and Simulation

近年来,灰色系统理论在各个领域中的应用愈发广泛.在灰色预测模型中,GM(1,1)模型最为核心与基础,但该模型对振荡序列难以进行模拟,且振荡序列往往无法通过准指数律检验,这削弱了GM(1,1)模型的应用范围.本文利用GM(1,1)模型对单调序列的模拟,对振荡序列的1-AGO序列建立 GM(1,1)模型.再通过引入修正项的IAGO操作,还原到对原振荡序列的模拟.建立了改进的GM(1,1)模型,弥补了传统GM(1,1)模型对振荡序列模拟的缺陷.

submitted time 2021-05-07 Hits4136Downloads434 Comment 0

2. chinaXiv:202104.00127 [pdf]

灰色系统GM(1,1)与三角函数耦合模型的研究

倪嘉雨; 叶林峰; 高德宏; 邓洋
Subjects: Mathematics >> Modeling and Simulation

灰色系统模型由于其具有简便、数学背景清晰等特点,在数学建模与近似计算等领域都有着十分广泛的应用。灰色系统模型的原理可以概括为利用时间响应函数来模拟数据序列的演化,而其中GM(1,1)模型作为最基础、最能体现灰色建模思想的一个模型,应用最广泛。传统的GM(1,1)模型的时间响应函数是以自然常数 的指数构造的函数,也正是由于这个特点,所以GM(1,1)模型具有较强的局限性,在实际应用中人们往往会将GM(1,1)模型的时间响应函数做一定的修正。其中,最重要的一种修正方法就是将原本的时间响应函数与其他能够描述数据序列性质的函数进行耦合,例如对于具有一定周期性或准周期性的数据序列,就可将原本的时间响应函数与三角函数耦合,构成GM(1,1)-三角函数耦合模型。本文便深入探讨了这种模型的可行性,提出了耦合模型时间响应函数中参数的估计方法,以及误差分析。

submitted time 2021-04-23 Hits4640Downloads411 Comment 0

3. chinaXiv:202002.00066 [pdf]

新型冠状病毒肺炎疫情的动力学分析和预测

诸葛昌靖; 张东艳; 杨武岳; 彭梁榕; 洪柳
Subjects: Mathematics >> Modeling and Simulation

基于经典动力学模型和模型参数自动优化算法, 本文分析了全国当前累计确诊感染病例数大于100(截止到2020年2月16日)的24个省市自治区, 以及湖北省除神农架以外的16个地市从2020年1月20日至2月16日的累计确诊病例数, 并对相应省市地区疫情可能的结束时间和总感染人数的进行了长期预测. 我们的研究表明, 在目前严防严控措施下, 全国大部分省市的疫情将于2月底前基本结束, 而湖北省内疫情也有望于3月中旬结束, 但是武汉市的疫情可能要持续到4月初. 通过对比公开数据与预测值, 我们建议加强对黑龙江、河北、江西、安徽、贵州和四川六省, 以及湖北省内武汉、荆州、鄂州、随州、天门和恩施六个地市的的监控, 以防疫情死灰复燃. 此外, 分析结果提示, 在疫情发展前期, 天津、河北、重庆、四川、海南和广西等省, 以及湖北省下辖多个地市可能存在着聚集性感染, 这有待于疫后进一步的流行病学调查确认.

submitted time 2020-02-25 Hits24686Downloads2576 Comment 0

4. 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 Hits18839Downloads1323 Comment 0

5. chinaXiv:201705.00968 [pdf]

Using associative neural network to interpret syndromes of Traditional Chinese Medicine

Xi Guangcheng Chen Jianxin Yi JianQiang
Subjects: Mathematics >> Modeling and Simulation

Millions of people benefit form Traditional Chinese Medicine TCM every day. Unfortunately till now TCM has not been accepted as science by world especially western people. Bian Zheng Lun Zhi is distillation of TCM. Syndrome is key in system of Bian Zheng Lun Zhi. Study about the syndrome is core of study of basic theory of TCM. We creatively interpret TCM through a view of cognitive science and take syndromes of TCM as concepts of brain. This paper try to introduce syndrome to western people in order to let western people understand our viewpoints more easily the best method is to adopt a manner that is easily understood by them already exists and has been thought to be right. So we employ neural network presented by foreign people as brain model instead of network presented by us Using two classic case of TCM we successfully clarify the three main properties of syndrome in TCM.

submitted time 2017-05-25 Hits5094Downloads2392 Comment 0

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