容格式：
Abstract
Introduction
Assumptions
Analysis of the problem
Task 1 : predicting survivorship
Task2 : achieving stability
….
Sensitivity analysis
Strengths
Weaknesses
Conclusion
References
Title(use Arial 14)
First author , second author , the other (use Arial 14)
Full address of first author . Including country and mail(use Arial 11)
Full address of second author . Including country and mail
List all distinct addresses in the same way
Keywords(use Arial 11)
Abstract
1985:
模型概述-考虑因素-使用理由
We modelled…. Since…–we used …. We included…which were to be chosen in order to…
假设条件-数据处理法
We assumed that…We used actual data to estimate realistic ranges on the parameters in the model.
评估标准-衡量法-得到结论-结论的可靠性
We defined…We then used…we found…We examined the results for different values of the mortality parameters and found them to be the same . Therefore ,our solution appears to be stable with respect to environmental conditions.
2000:
背景设置-模型引入
…in order to determine …, we develop models using…
解决问题-模型解决（层次排比）
For the solution of …, we develop… model based … to … . For the solution of … , we employ…What is more , a self-adaptive traffic light is employed to …according to …
模型检验-模型修正
By comparison of …simulation results , the models are evaluated . …is formulated to judge which solution is effective .
2002:
The task is to … we begin by constructing a model of … base on … Using this model we can … Using… , we model … through … and obtain … we compare the performance of our model in … simulations show that …
2001:
We examine the … . Such evacuations been required due to … . in order to … , we begin with an analysis of … . For a more realistic estimate , including the effects of … , we formulate models of … . The model we construct is based on … .This model leads to a … and it further show that … what’ more , it agrees with …
2004:
（修正递进式模型摘要模板）
The purpose of this paper is to propose … . We propose that … . To build a solid foundation , we define and test a simple model for … . We then develop …system , but we find it would be far from optimal in practice . We then propose that the best model is one that adapts to … . We implement … . We simulate the …with …and we find this system quickly converges to a nearly optimal solution subject to our constraints . It is , however , sensitive to some parameters . We discuss the effects of these findings on the expected effectiveness of the system in a real environment . We conclude that … is a good solution .
问题分析句式：
… is a real-life common phenomenon with many complexities .
For a better view of … , we …
To give a clear expression, we will introduce the method presented by …
模型引入句式：
In this paper , we present … model to simulate efficient methods for …
We also apply … methods to solve …
We address the problem of …. through ….
We formulate the problem as …
We formulate a … model to account for …
Base on … , we establish a model ….
We build a model to determine …
We modify the model to reflect …
To provide a more complete account for … , ... model has been employed .
In this paper , in order to … , we design a … model based on …
We propose a solution that …
We have come up with an … for … and
Strong evidence of ... , and powerful models have been created to estimate ...
模型推进：
… will scale up to an effective model for …
模型求解：
We employ …, one based on …and the other …, whose results agree closely.
To combat this , we impose …
结合数据：
Using data from … , we determine …
To ground this model in reality , we incorporate extensive demographic data ….
We use data assembled by …
Using a wide scale regression , we found that …
We extrapolate from longevity data and explore the long-term behavior of …
The base we developed was based off real-life data that gathered by …
We estimate these characteristic numbers for a representative sample of …
We fit the modified model to data , we conclude that …
By statistical processing to results of …
By analyzing the … on the basis of historic data in the same way mentioned in …
结果给出句式：
Results of this computation are presented , and ….
We elicit that a conclusion …
We conclude with a series of recommendations for …
Given a …deviation in the value of the parameter , we calculate the percentage change in the value that the system converges to …
As we can find out , in the situation of …. , …. is subject to the logistic regression .
We conclude through analyzing that ….
it is apparent that …
Through comparing the … , we conclude that …
According to the laws of … , we draw a conclusion of …
From the formula , we know that …
Thus we arrive at the conclusion :
We elicit that a conclusion …
As a consequence , we can get …
模型可行性：
Our suggested solution , which is easy to ….
Since our model is based on … it can be applied to …
Importantly , we use some practical data to test our model and analysis its stability , we simulate this model and receive a well effect .
Therefore , we trust this model as an accurate testing ground for …
Our algorithm is broad enough to accommodate various …
定理可靠说明：
That is the theoretical basis for … in many application areas .
模型简化
With further simplification, utilizing … we can reach …
承上启下：
In addition to the model , we also discuss …
Because the movement of … operates by the same laws and equations as the movement of … , we can ….
Based on the above discussion, considering …., let’s …
误差句式：
… does not deviate more than … from the target value .
Theoretically , error due to … should not play a tremendous role under our model .
Up to this point , we have made many approximations , not all of which are justified theoretically , but the results of algorithm are quite reasonable .
This is a na?ve approach which may mot ensure the …. , however if we … , the error is negligible .
Context:
程给出：
We derive the equation expressing the … as a function of… we have
A simple formula determined by the … is given by the equation :
… can be written as the following system of equations :
In particular , the … is defined in terms of … ,
问题A：除非超车否则靠右行驶的交通规则 在一些汽车靠右行驶的国家（比如美国，中国等等），多车道的高速公路常常遵循以下原则：司机必须在最右侧驾驶，除非他们正在超车，超车时必须先移到左侧车道在超车后再返回。建立数学模型来分析这条规则在低负荷和高负荷状态下的交通路况的表现。你不妨考察一下流量和安全的权衡问题,车速过高过低的限制，或者这个问题陈述中可能出现的其他因素。这条规则在提升车流量的方面是否有效？如果不是，提出能够提升车流量、安全系数或其他因素的替代品（包括完全没有这种规律）并加以分析。在一些国家，汽车靠左形式是常态，探讨你的解决方案是否稍作修改即可适用，或者需要一些额外的需要。最后，以上规则依赖于人的判断，如果相同规则的交通运输完全在智能系统的控制下，无论是部分网络还是嵌入使用的车辆的设计，在何种程度上会修改你前面的结果？ 问题B：大学传奇教练 体育画报是一个为运动爱好者服务的杂志，正在寻找在整个上个世纪的“史上最好的大学教练”。建立数学模型选择大学中在一下体育项目中最好的教练：曲棍球或场地曲棍球，足球，棒球或垒球，篮球，足球。 时间轴在你的分析中是否会有影响？比如1913年的教练和2013年的教练是否会有所不同？清晰的对你的指标进行评估，讨论一下你的模型应用在跨越性别和所有可能对的体育项目中的效果。展示你的模型中的在三种不同体育项目中的前五名教练。 除了传统的MCM格式，准备一个1到2页的文章给体育画报，解释你的结果和包括一个体育迷都明白的数学模型的非技术性解释。 使用网络测量的影响和冲击 学术研究的技术来确定影响之一是构建和引文或合著网络的度量属性。与人合写一手稿通常意味着一个强大的影响力的研究人员之间的联系。最著名的学术合作者是20世纪的数学家保罗鄂尔多斯曾超过500的合作者和超过1400个技术研究论文发表。讽刺的是,或者不是,鄂尔多斯也是影响者在构建网络的新兴交叉学科的基础科学,尤其是，尽管他与Alfred Rényi的出版物“随即图标”在1959年。鄂尔多斯作为合作者的角色非常重要领域的数学,数学家通常衡量他们亲近鄂尔多斯通过分析鄂尔多斯的令人惊讶的是大型和健壮的合著网络网站(见http:// https://www.doczj.com/doc/8f13660049.html,/enp/)。保罗的与众不同、引人入胜的故事鄂尔多斯作为一个天才的数学家,才华横溢的problemsolver,掌握合作者提供了许多书籍和在线网站(如。,https://www.doczj.com/doc/8f13660049.html,/Biographies/Erdos.html)。也许他流动的生活方式,经常住在带着合作者或居住,并给他的钱来解决问题学生奖,使他co-authorships蓬勃发展并帮助构建了惊人的网络在几个数学领域的影响力。为了衡量这种影响asErdos生产,有基于网络的评价工具,使用作者和引文数据来确定影响因素的研究,出版物和期刊。一些科学引文索引,Hfactor、影响因素,特征因子等。谷歌学术搜索也是一个好的数据工具用于网络数据收集和分析影响或影响。ICM 2014你的团队的目标是分析研究网络和其他地区的影响力和影响社会。你这样做的任务包括: 1)构建networkof Erdos1作者合著者(你可以使用我们网站https://files.oak https://www.doczj.com/doc/8f13660049.html,/users/grossman/enp/Erdos1.htmlor的文件包括Erdos1.htm)。你应该建立一个合作者网络Erdos1大约有510名研究人员的文件,与鄂尔多斯的一篇论文的合著者,他但不包括鄂尔多斯。这将需要一些技术数据提取和建模工作获
For office use only T1________________ T2________________ T3________________ T4________________ Team Control Number 55069 Problem Chosen A For office use only F1________________ F2________________ F3________________ F4________________ 2017 MCM/ICM Summary Sheet The Rehabilitation of the Kariba Dam Recently, the Institute of Risk Management of South Africa has just warned that the Kariba dam is in desperate need of rehabilitation, otherwise the whole dam would collapse, putting 3.5 million people at risk. Aimed to look for the best strategy with the three options listed to maintain the dam, we employ AHP model to filter factors and determine two most influential criteria, including potential costs and benefits. With the weight of each criterion worked out, our model demonstrates that option 3is the optimal choice. According to our choice, we are required to offer the recommendation as to the number and placement of the new dams. Regarding it as a set covering problem, we develop a multi-objective optimization model to minimize the number of smaller dams while improving the water resources management capacity. Applying TOPSIS evaluation method to get the demand of the electricity and water, we solve this problem with genetic algorithm and get an approximate optimal solution with 12 smaller dams and determine the location of them. Taking the strategy for modulating the water flow into account, we construct a joint operation of dam system to simulate the relationship among the smaller dams with genetic algorithm approach. We define four kinds of year based on the Kariba’s climate data of climate, namely, normal flow year, low flow year, high flow year and differential year. Finally, these statistics could help us simulate the water flow of each month in one year, then we obtain the water resources planning and modulating strategy. The sensitivity analysis of our model has pointed out that small alteration in our constraints (including removing an important city of the countries and changing the measurement of the economic development index etc.) affects the location of some of our dams slightly while the number of dams remains the same. Also we find that the output coefficient is not an important factor for joint operation of the dam system, for the reason that the discharge index and the capacity index would not change a lot with the output coefficient changing.
Camping along the Big Long River Summary In this paper, the problem that allows more parties entering recreation system is investigated. In order to let park managers have better arrangements on camping for parties, the problem is divided into four sections to consider. The first section is the description of the process for single-party's rafting. That is, formulating a Status Transfer Equation of a party based on the state of the arriving time at any campsite. Furthermore, we analyze the encounter situations between two parties. Next we build up a simulation model according to the analysis above. Setting that there are recreation sites though the river, count the encounter times when a new party enters this recreation system, and judge whether there exists campsites available for them to station. If the times of encounter between parties are small and the campsite is available, the managers give them a good schedule and permit their rafting, or else, putting off the small interval time t until the party satisfies the conditions. Then solve the problem by the method of computer simulation. We imitate the whole process of rafting for every party, and obtain different numbers of parties, every party's schedule arrangement, travelling time, numbers of every campsite's usage, ratio of these two kinds of rafting boats, and time intervals between two parties' starting time under various numbers of campsites after several times of simulation. Hence, explore the changing law between the numbers of parties (X) and the numbers of campsites (Y) that X ascends rapidly in the first period followed by Y's increasing and the curve tends to be steady and finally looks like a S curve. In the end of our paper, we make sensitive analysis by changing parameters of simulation and evaluate the strengths and weaknesses of our model, and write a memo to river managers on the arrangements of rafting. Key words: Camping；Computer Simulation; Status Transfer Equation
The Keep-Right-Except-To-Pass Rule Summary As for the first question, it provides a traffic rule of keep right except to pass, requiring us to verify its effectiveness. Firstly, we define one kind of traffic rule different from the rule of the keep right in order to solve the problem clearly; then, we build a Cellular automaton model and a Nasch model by collecting massive data; next, we make full use of the numerical simulation according to several influence factors of traffic flow; At last, by lots of analysis of graph we obtain, we indicate a conclusion as follow: when vehicle density is lower than 0.15, the rule of lane speed control is more effective in terms of the factor of safe in the light traffic; when vehicle density is greater than 0.15, so the rule of keep right except passing is more effective In the heavy traffic. As for the second question, it requires us to testify that whether the conclusion we obtain in the first question is the same apply to the keep left rule. First of all, we build a stochastic multi-lane traffic model; from the view of the vehicle flow stress, we propose that the probability of moving to the right is 0.7and to the left otherwise by making full use of the Bernoulli process from the view of the ping-pong effect, the conclusion is that the choice of the changing lane is random. On the whole, the fundamental reason is the formation of the driving habit, so the conclusion is effective under the rule of keep left. As for the third question, it requires us to demonstrate the effectiveness of the result advised in the first question under the intelligent vehicle control system. Firstly, taking the speed limits into consideration, we build a microscopic traffic simulator model for traffic simulation purposes. Then, we implement a METANET model for prediction state with the use of the MPC traffic controller. Afterwards, we certify that the dynamic speed control measure can improve the traffic flow . Lastly neglecting the safe factor, combining the rule of keep right with the rule of dynamical speed control is the best solution to accelerate the traffic flow overall. Key words：Cellular automaton model Bernoulli process Microscopic traffic simulator model The MPC traffic control
C和D 2015 ICM问题C 组织中的人力资本管理 构建一个组织填充好，有才华的，训练有素的人是成功的关键之一。但是这样做，组织需要做更多的招聘和雇用最好的候选人–也需要保持良好的人，让他们适当的训练并放在合适的位置，最终目标新员工来取代那些离开组织。个人发挥独特的作用，在他们的组织，正式和非正式的。因此，从组织个体离开留下重要的信息和功能组件丢失，需要更换。这是真正的运动队，商业公司，学校，政府，和几乎任何正式的团体或组织的人。 人力资源（HR）专家帮助高层领导通过改进保留和激励，管理人员协调培训，并建立良好的团队。特别是，领导人寻求建立一个有效的组织结构，人们被分配到适当的位置他们的天赋和经验，以及有效的沟通系统，以促进发展创新的理念、优质的产品（商品或服务）。这些人才管理和人力资源管理团队建设方面正在对许多现代组织。 在一个组织内人力资本的流体网络管理人员需要了解忠诚于公司和亚群；在工作场所建立信任；管理的形成，溶解和保持人与人之间的正式和非正式的关系。当人们离开其他工作或退休所取代，由此产生的湍流是统称为组织“流失”。你的团队你的人力资源经理要求在信息协同制造发展了一个理解流失的框架和模型（ICM）的370人的组织。ICM是一个高度竞争的市场，导致具有挑战性，有效地管理其人力资本的相关问题。 人力资源经理要地图人力资本在组织通过建立网络模型。这里有一些你的公司面临的问题： 1。ICM的目的是在其早期阶段的流失的风险，因为它是获得一个员工在职业生涯早期而不是提高文化一旦有了忠诚的便宜。这是更高效的开始而不是提供激励措施来阻止人们离开有一个积极的员工。 2。一个工人更容易流失，如果他或她与其他前 谁有生产员工。因此，从员工流失似乎弥漫 员工，所以识别那些可能流失是有价值的信息 防止进一步的搅动。 3。一个问题是员工人力资源匹配到正确的位置，使自己的知识和能力可以最大化。目前每个员工基于绩效的主管判断年度评估。这些评价是目前不是由人力资源办公室。
Team Control Number For office use only 13215 For office use only T1 ________________ F1 ________________ T2 ________________ F2 ________________ T3 ________________ Problem Chosen F3 ________________ T4 ________________ F4 ________________ C 2012 Mathematical Contest in Modeling (MCM) Summary Sheet (Attach a copy of this page to each copy of your solution paper.) Type a summary of your results on this page. Do not include the name of your school, advisor, or team members on this page. Message Network Modeling for Crime Busting Abstract A particularly popular and challenging problem in crime analysis is to identify the conspirators through analysis of message networks. In this paper, using the data of message traffic, we model to prioritize the likelihood of one’s being conspirator, and nominate the probable conspiracy leaders. We note a fact that any conspirator has at least one message communication with other conspirators, and assume that sending or receiving a message has the same effect, and then develop Model 1, 2 and 3 to make a priority list respectively and Model 4 to nominate the conspiracy leader. In Model 1, we take the amount of one’s suspicious messages and one’s all messages with known conspirators into account, and define a simple composite index to measure the likelihood of one’s being conspirator. Then, considering probability relevance of all nodes, we develop Model 2 based on Law of Total Probability . In this model, probability of one’s being conspirator is the weight sum of probabilities of others directly linking to it. And we develop Algorithm 1 to calculate probabilities of all the network nodes as direct calculation is infeasible. Besides, in order to better quantify one’s relationship to the known conspirators, we develop Model 3, which brings in the concept “shortest path” of graph theory to create an indicator evaluating the likelihood of one’s being conspirator which can be calculated through Algorithm 2. As a result, we compare three priority lists and conclude that the overall rankings are similar but quite changes appear in some nodes. Additionally, when altering the given information, we find that the priority list just changes slightly except for a few nodes, so that we validate the models’ stability. Afterwards, by using Freeman’s centrality method, we develop Model 4 to nominate three most probable leaders: Paul, Elsie, Dolores (senior manager). What’s more, we make some remarks about the models and discuss what could be done to enhance them in the future work. In addition, we further explain Investigation EZ through text and semantic network analysis, so to illustrate the models’ capacity of applying to more complicated cases. Finally, we briefly state the application of our models in other disciplines.
2019 MCM/ICM Summary Sheet (Your team's summary should be included as the first page of your electronic submission.) Type a summary of your results on this page. Do not include the name of your school, advisor , or team members on this page. Ecosystems provide many natural processes to maintain a healthy and sustainable environment after human life. However, over the past decades, rapid industrial development and other anthropogenic activities have been limiting or removing ecosystem services. It is necessary to access the impact of human activities on biodiversity and environmental degradation. The main purpose of this work is to understand the true economic costs of land use projects when ecosystem services are considered. To this end, we propose an ecological service assessment model to perform a cost benefit analysis of land use development projects of varying sites, from small-scale community projects to large national projects. We mainly focus on the treatment cost of environmental pollution in land use from three aspects: air pollution, solid waste and water pollution. We collect pollution data nationwide from 2010 to 2015 to estimate economic costs. We visually analyze the change in economic costs over time via some charts. We also analyze how the economic cost changes with time by using linear regression method. We divide the data into small community projects data (living pollution data) and large natural data (industrial pollution data). Our results indicate that the economic costs of restoring economical services for different scales of land use are different. For small-scale land, according to our analysis, the treatment cost of living pollution is about 30 million every year in China. With the rapid development of technology, the cost is lower than past years. For large-scale land, according to our analysis, the treatment cost of industrial pollution is about 8 million, which is lower than cost of living pollution. Meanwhile the cost is trending down due to technology development. The theory developed here provides a sound foundation for effective decision making policies on land use projects. Key words: economic cost , ecosystem service, ecological service assesment model, pollution. Team Control Number For office use only For office use only T1 ________________ F1 ________________ T2 ________________ F2 ________________ T3 ________________ Problem Chosen F3 ________________ T4 ________________ F4 ________________ E
点评：航空货运问题 一、基本参数 1、货机：假设均匀分布 每天三架货机。 2、工作时间5：00—20：00设置为 t ：[0，15]？ 每天货机到达时间：5：00—20：00； 一工作组装满装卸场：6小时；一货机装满：3小时； 装卸台的容量：1.5货机； 3、费用系数： 停机费（等待装货）：15000元/小时架 一工作组：每小时9000元；二工作组：每小时12000元 4、服务原则：假设先来先服务 二、模型建立：概率计算模型 （一）概率分布 1、三架货机到达的时刻3,2,1,=i t i 服从[0，15]上的均匀分布，则： 密度函数：()1 ,01515 f t t = ≤≤ 分布函数：(),01515 t F t t = ≤≤ 2、设τ,δ,ε分别是首架货机到达时刻、第一架与第二架间隔、第二架与第三架间隔，
（1）τ的分布函数 3 31321321321321321))(1(1))(1(1)()()(1),,(1) ()()},,(min{) ()(1t F t t P t t P t t P t t P t t t t t t P t t t t t t P t t t t t t P t t t t P t P t F t --=≤--=>>>-=>>>-=≤?≤?≤-Ω=≤?≤?≤=≤=≤=ττ τ 的密度函数： ()()()1125 15151)151(3]1[3)(')(2 22 11-=-=-==t t t f t F t F t f t t ττ ]15,0[∈t （2）其余两货机到达与第一个到达的货机的间隔21,t t ??在0到15-τ之间是均匀分布的 于是： τ -=?151)(t f i t , τ-≤≤150t ；τ-=?15)(t t F i t , τ-≤≤150t ，i =1,2 δ 的密度函数 /121212()()()1() 1()() F t P t P t t t t P t t t t P t t P t t δτδ=≤=?≤?≤=-?>?>=-?>?> 221)](1[1)](1[11t F t t P t ?--=≤?--= ()()2//15152)()](1[2)(')(11---= -==??τττδτδt t f t F t F t f t t （3）第三架货机到达与第二个到达的货机的间隔ε在0和15-δ-τ之间是均匀分布的， 于是： ε 的密度函数
摘要 第一段：写论文解决什么问题 1．问题的重述 a. 介绍重点词开头： 例1：“Hand move” irrigation, a cheap but labor-intensive system used on small farms, consists of a movable pipe with sprinkler on top that can be attached to a stationary main. 例2:……is a real-life common phenomenon with many complexities. 例3：An (effective plan) is crucial to……… b. 直接指出问题： 例1：We find the optimal number of tollbooths in a highway toll-plaza for a given number of highway lanes: the number of tollbooths that minimizes average delay experienced by cars. 例2：A brand-new university needs to balance the cost of information technology security measures with the potential cost of attacks on its systems. 例3：We determine the number of sprinklers to use by analyzing the energy and motion of water in the pipe and examining the engineering parameters of sprinklers available in the market. 例4: After mathematically analyzing the ……problem, our modeling group would like to present our conclusions, strategies, (and recommendations )to the ……. 例5：Our goal is... that (minimizes the time )………. 2．解决这个问题的伟大意义 反面说明。如果没有…… Without implementing defensive measure, the university is exposed to an expected loss of $8.9 million per year. 3．总的解决概述 a．通过什么方法解决什么问题 例：We address the problem of optimizing amusement park enjoyment through distributing Quick Passes (QP), reservation slips that ideally allow an individual to spend less time waiting in line. b．实际问题转化为数学模型 例1 We formulate the problem as a network flow in which vertices are the locations of escorts and wheelchair passengers. 例2 : A na?ve strategy would be to employ the minimum number of escorts to guarantee that all passengers reach their gates on time. c.将问题分阶段考虑 例3：We divide the jump into three phases: flying through the air, punching through the stack, and landing on the ground. 第二、三段：具体分析 1．在什么模型中/ 建立了什么模型 a. 主流模型 例1：We formulate a differential model to account for the rates of change of these uses, and how this change would affect the overall consumption of water within the studied region.
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