小麦发育后期茎秆抗倒性的数学模型探析

围绕小麦发育后期茎秆抗倒性的数学模型建立的问题,首先,运用回归分析方法,得到了基于统计的倒伏指数的估计.然后,运用相关分析方法,并引入斐波那契数列及Euclidean距离,分析了小麦抗倒伏性与其茎秆形态参数之间的关系,得到了理想的小麦株型结构.最后,运用平衡理论、挠曲线近似方程、最小势能原理及弯矩平衡原理,考虑小麦自重和风载的共同作用,从平衡理论与弹性理论的角度建立了小麦茎秆抗倒伏性的精确模型.利用该模型结合估计的倒伏指数,对临界倒伏风速进行计算,结果验证了模型的有效性.     

小麦蜡熟期茎杆抗倒伏数学模型的建立

以物理学力学理论为基础,在考虑小麦穗自重,风力大小、风力大小、方向及作用点的因素下,将茎杆状态分为无风情况下的静态过程和有风情况下的动态过程,分别建立小麦蜡熟期茎杆的静态和动态抗倒伏模型.提出合理假设,得到2008年和2011年数据中各品种的机械强度、茎杆鲜重和重心高度的计算公式,再结合已给的倒伏指数公式,计算得到各小麦品种的倒伏指数;接下来,通过斯皮尔曼相关系数分判断倒伏指数与外部特征因素的相关性大小;最后,在考虑穗自重,风力大小、方向及作用点,茎杆变形能的影响因素下,分别建立小麦抗倒伏静态模型和动态模型.其中静态模型以临界力为计算目标,动态模型同时考虑穗自重和风载因素,最终将静态模型和动态模型结合作为小麦抗倒伏模型.文章最后利用已知数据,计算得到抗倒伏模型各个参数,同时对动态模型进行仿真,得到在一定风速下茎杆摆动的运动轨迹.在此基础上,考虑到该模型为典型的非线性动力模型,利用相平面分析法发现存在明显混沌现象,并进一步找出可能导致混沌的相关特性参数.     

小麦发育后期茎秆抗倒伏性的数学模型

对小麦发育后期茎秆抗倒伏性进行了研究.建立了基于茎秆密度和机械强度的改进型抗倒伏指数模型;采用相关系数、通径分析、灰色关联分析三种方法对倒伏指数与外部形态的关联性进行了分析;提出了理想株型结构的定义,建立双目标优化模型探讨理想模型的数值解;分别从茎秆线密度线性变化、分节几何性质均匀以及分节物理性质均匀的情况下获得三个抗倒伏模型;最后为小麦茎秆抗倒伏研究提出了建议.     

对小麦发育后期茎秆抗倒性问题的研究

针对小麦发育后期茎秆抗倒伏性问题,首先运用了数理统计与分析的相关知识,建立了各品种小麦的抗倒伏指数模型并对其进行了求解;其次,通过建立相关性系数模型并结合SPSS软件分析研究了抗倒伏指数与茎秆外部形态特征之间的关系;然后,建立了以抗倒伏能力最强和经济系数最大为目标的双目标优化模型来确定不同单穗重小麦的理想株型结构;最后,建立了基于力学分析的小麦茎秆抗倒伏性能的综合评价模型与抗倒伏风速模型.     

Solving multistage stochastic network programs on massively parallel computers

Multi-stage stochastic programs are typically extremely large, and can be prohibitively expensive to solve on the computer. In this paper we develop an algorithm for multistage programs that integrates the primal-dual row-action framework with proximal minimization. The algorithm exploits the structure of stochastic programs with network recourse, using a suitable problem formulation based on split variables, to decompose the solution into a large number of simple operations. It is therefore possible to use massively parallel computers to solve large instances of these problems. The algorithm is implemented on a Connection Machine CM-2 with up to 32K processors. We solve stochastic programs from an application from the insurance industry, as well as random problems, with up to 9 stages, and with up to 16392 scenarios, where the deterministic equivalent programs have a half million constraints and 1.3 million variables. Research partially supported by NSF grants CCR-9104042 and SES-91-00216, and AFOSR grant 91-0168. Computing resources were made available by AHPCRC at the University of Minnesota, and by NPAC at Syracuse University, New York.     

A Bayesian approach for predicting match outcomes: The 2006 (Association) Football World Cup

In this paper we propose a Bayesian methodology for predicting match outcomes. The methodology is illustrated on the 2006 Soccer World Cup. As prior information, we make use of the specialists’ opinions and the FIFA ratings. The method is applied to calculate the win, draw and loss probabilities at each match and also to simulate the whole competition in order to estimate classification probabilities in group stage and winning tournament chances for each team. The prediction capability of the proposed methodology is determined by the DeFinetti measure and by the percentage of correct forecasts.     

A mixed-method optimisation and simulation framework for supporting logistical decisions during offshore wind farm installations

With a typical investment in excess of £100 million for each project, the installation phase of offshore wind farms (OWFs) is an area where substantial cost-reductions can be achieved; however, to-date there have been relatively few studies exploring this. In this paper, we develop a mixed-method framework which exploits the complementary strengths of two decision-support methods: discrete-event simulation and robust optimisation. The simulation component allows developers to estimate the impact of user-defined asset selections on the likely cost and duration of the full or partial completion of the installation process. The optimisation component provides developers with an installation schedule that is robust to changes in operation durations due to weather uncertainties. The combined framework provides a decision-support tool which enhances the individual capability of both models by feedback channels between the two, and provides a mechanism to address current OWF installation projects. The combined framework, verified and validated by external experts, was applied to an installation case study to illustrate the application of the combined approach. An installation schedule was identified which accounted for seasonal uncertainties and optimised the ordering of activities.     

小麦发育后期茎秆抗倒伏问题研究

围绕小麦抗倒伏问题,综合运用数据预处理、相关性分析、数据拟合、数理方程、微分方程等方法,根据已有的抗倒伏模型,进行了模型修正,运用修正的模型,计算了六种小麦的倒伏指数,计算结果与试验结论基本吻合,并从生活常识的角度对模型的合理性进行论证,在对小麦茎秆性状相关性分析中,讨论了小麦最优性状特征,得出不同穗重下的最优株型结构,在考虑麦穗自重的前提下,进行力矩分析,运用最小势能原理进行理论推导,建立茎秆抗倒伏数理方程模型,并从数值计算和图形分析两个方面对模型的合理性进行了论证.     

小麦茎秆抗倒性的数学模型研究

利用多元统计分析和微分方程建立了小麦发育后期茎秆抗倒伏的数学模型.首先,对实验所得的数据进行了预处理,建立了倒伏指数的相关模型,并在给定穗重的条件下,模拟出理想的株型结构;然后,对小麦茎秆进行受力分析,建立小麦倒伏临界力的微分方程,算出腊熟期各品种小麦的抗倒伏风速;最后,对所建模型以及相关问题和结果进行总结分析,并结合实际提出小麦育种的一些建议.     

Soil depth and soil production

Soil column depth is predicted over time scales up to a million years based on dynamics at the pore scale. The power law result integrates result for solute transport from percolation theory with typical flow velocities. Verification was based on studied soils from 14 regions worldwide over time scales from decades to a million years. The time derivative of the soil depth generates the soil production function as a function of depth. Comparison with soil production data from five locations, over similar time scales, verifies the accuracy of the predicted power to within 2%. The prediction thus unites within one framework time scales of seconds with a million years. The results allow calculation of the effects of physical soil removal on the rates of silicate weathering at the base of the column, important inputs to the global carbon cycle, neotectonics, and drainage basin evolution. © 2015 Wiley Periodicals, Inc. Complexity 21: 42–49, 2016     

A ratings based Poisson model for World Cup soccer simulation

In this paper a method is suggested for predicting the distribution of scores in international soccer matches, treating each team’s goals scored as independent Poisson variables dependent on the Fédération Intemationale de Football Association (FIFA) rating of each team, and the match venue. The results of a Poisson regression to estimate parameters for this model were used to simulate matches played during the 1998 World Cup tournament. For the model to be a more effective predictor, some manual adjustments must be made to the ratings data. The predictions of the model were placed on a web page to create interest in applications of mathematics, and proved popular with the general public.     

Proximal minimizations with D-functions and the massively parallel solution of linear network programs

This paper discusses the massively parallel solution of linear network programs. It integrates the general algorithmic framework of proximal minimization with D-functions (PMD) with primal-dual row-action algorithms. Three alternative algorithmic schemes are studied: quadratic proximal point, entropic proximal point, and least 2-norm perturbations. Each is solving a linear network problem by solving a sequence of nonlinear approximations. The nonlinear subproblems decompose for massively parallel computing. The three algorithms are implemented on a Connection Machine CM-2 with up to 32K processing elements, and problems with up to 16 million variables are solved. A comparison of the three algorithms establishes their relative efficiency. Numerical experiments also establish the best internal tactics which can be used when implementing proximal minimization algorithms. Finally, the new algorithms are compared with an implementation of the network simplex algorithm executing on a CRAY Y-MP vector supercomputer.     

沙子的开采

为一个1000×500(米)地区沙子的开采进行工程设计和评估.根据该地区20×10个网点处有关数据,估算该地区的沙的储量是210万吨.在每月10万吨的开挖量的限制条件和考虑1%的月贴现率下,引入开采每吨沙土所获利润函数,确定开采沙子的施工原则是实现该函数由大到小.然后照顾施工方便设计每月具体工程方案,计算出整个工程需投资2364.6万元,工期30个月.可采沙195.54万吨,获利润近1500万元,利润率在60%以上.     

A Scalable Parallel Interior Point Algorithm for Stochastic Linear Programming and Robust Optimization

We present a computationally efficient implementation of an interior point algorithm for solving large-scale problems arising in stochastic linear programming and robust optimization. A matrix factorization procedure is employed that exploits the structure of the constraint matrix, and it is implemented on parallel computers. The implementation is perfectly scalable. Extensive computational results are reported for a library of standard test problems from stochastic linear programming, and also for robust optimization formulations.The results show that the codes are efficient and stable for problems with thousands of scenarios. Test problems with 130 thousand scenarios, and a deterministic equivalent linear programming formulation with 2.6 million constraints and 18.2 million variables, are solved successfully.     

“小麦发育后期茎秆抗倒性的数学模型”综述

2011年第8届全国研究生数学建模竞赛C题是一个农业生产中小麦倒伏问题,在给出3年原始测量数据的基础上要求建立小麦发育后期茎秆抗倒性的数学模型,内容包括小麦性状数据处理和弹性力学模型.综述为C题竞赛总结,含问题的提出、问题的解答与评阅情况、存在问题及研究建议.     

Wildfire fuel management: Network-based models and optimization of prescribed burning

Wildfires are a common phenomenon on most continents. They have occurred for an estimated 60 million years and are part of a regular climatic cycle. Nevertheless, wildfires represent a real and continuing problem that can have a major impact on people, wildlife and the environment. The intensity and severity of wildfires can be reduced through fuel management activities. The most common and effective fuel management activity is prescribed burning. We propose a multi-period optimization framework based on mixed integer programming (MIP) techniques to determine the optimal spatial allocation of prescribed burning activities over a finite planning horizon. In contrast to the existing fuel management optimization literature, we model fuel accumulation with Olson’s equation. To capture potential fire spread along with irregular landscape connectivity considerations, we use a graph-theoretical approach that allows us to exploit graph connectivity measures (e.g., the number of connected components) as optimization objectives. The resulting mathematical programs can be tackled by general purpose MIP solvers, while for handling larger instances we propose a simple heuristic. Our computational experiments with test instances constructed based on real-life data reveal interesting insights and demonstrate the advantages and limitations of the proposed approaches.     

Some heuristics about the ecosystem of mathematics research data

Like in other sciences, research data play a growing role in mathematics, but in contrast to classical objects like measurements in physics they are much more heterogeneous. They may take the shape of abstract objects like the collection of integer sequences in OEIS, algorithms and their implementations as mathematical software, libraries of test problems or statistical data. From an infrastructure viewpoint, which aims at sustainable and connected data repositories which facilitate researchers to use existing information efficiently, it is essential to define an appropriate framework that allows not just storage but also connection and retrieval of the various types of data. Recently, there have been promising attempts to define standards for mathematical software, but the general task remains a big challenge, which is also addressed within the recently initiated GDML working group of the IMU. This is especially important in the fields of applied mathematics where research is often connected to research data originating from applications. The goal of this talk is a first attempt to analyse the diverse ecosystem of research data based on reference data from zbMATH. This approach has worked quite well for mathematical software, resulting in the formation of the swMATH database. Though reference data involve always a bias, the collected information of about 16 million reference data in zbMATH may be useful to identify the recent needs of researchers in different fields pertaining mathematical research data, and we discuss several aspects of such an analysis. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mixtures of truncated basis functions

In this paper we propose a framework, called mixtures of truncated basis functions (MoTBFs), for representing general hybrid Bayesian networks. The proposed framework generalizes both the mixture of truncated exponentials (MTEs) framework and the Mixture of Polynomials (MoPs) framework. Similar to MTEs and MoPs, MoTBFs are defined so that the potentials are closed under combination and marginalization, which ensures that inference in MoTBF networks can be performed efficiently using the Shafer-Shenoy architecture.Based on a generalized Fourier series approximation, we devise a method for efficiently approximating an arbitrary density function using the MoTBF framework. The translation method is more flexible than existing MTE or MoP-based methods, and it supports an online/anytime tradeoff between the accuracy and the complexity of the approximation. Experimental results show that the approximations obtained are either comparable or significantly better than the approximations obtained using existing methods.     

Multi-decisions rating model: Establishing rescue policies for Regional Drinking Water Companies (PDAMs) in Indonesia

Fresh water is abundant in Indonesia, but only about 20% out of more than 200 million of its population have access to clean water supplied by 306 Regional Drinking Water Companies (PDAMs) around the country. The poor performance of most PDAMs is due to high level of debt, lack of investment, and inefficient operations. On one hand, the PDAMs need to increase its coverage capacity but on the other hand they have been operating under unfavorable regulated tariff policies. A government team involving the Indonesia Water Enterprise Association (PERPAMSI) has developed a multi-criteria model to rate the PDAMs, grouped them based on their scores, and formulated common policies for each group. Unfortunately, the recommended policies do not appear to be specific enough to make them useful. This paper proposes improvements to the original model which used the Analytic Hierarchy Process (AHP) while maintaining the original priority judgments. Model-1 is the AHP representation of the original model, Model-2 is similar to Model-1 with the principle of hierarchic composition satisfied, and Model-3 is a framework for multi-decisions decision making involving clustering the PDAMs based on their business performance. Model-2 did not prove useful for identifying specific group policies that fit the need of every PDAM in a given group. Model-3 enables one to identify a specific policy that is applicable to either all the PDAMs or those grouped as a certain cluster by rating them based on a set of criteria that is relevant to that policy. The results of the three models are evaluated and some examples of using the Model-3 framework to rate the PDAMs, each with a specific policy in mind, are provided.