北京时间2016年4月12日，美国（国际）大学生数学建模竞赛与交叉学科数学建模竞赛(MCM/ICM)官方网站揭晓了2016年美赛结果。MCM/ICM是面向大学生和高中生的著名国际性赛事，每年举行一次，2015年有来自17个国家的917个院校共7636个团队参加了竞赛。本年度竞赛于北京时间2016年1月29日（农历月腊月二十）9点至2月2日10点进行。

    北师大系统科学学院、政府管理学院师生组织了多个队伍（部分组有其他院系学生参加）参加了本年度比赛，同学们经过4天的艰苦鏖战，出色完成竞赛要求的论文，最终取得了好的成绩。截至目前获悉，以管理科学专业同学为主要参赛人员的队伍已经获得4项国际一等奖(Meritorious Winner)和3项国际二等奖(Honorable Mention)。在此，向获奖同学表示祝贺，也向给与指导建议的教师表示感谢。

    MCM/ICM旨在发展并提升学生的解决交叉学科问题的能力和写作论文的能力。学生需组队参与，形成一个共同分享知识与能力的团队环境，锻炼同学们的组织协调能力。参加这项赛事一直是我院和政府管理学院的传统，每年均组织多个队伍参加。

    本次涉及管理科学专业的一等奖获得者名单如下：

    （1）冯业倩、张唯佳、张众

    （2）李雪阳、丁方洁（非管理科学专业）、刘馨儿（非管理科学专业）

    （3）刘之新、刘炫宇、熊慧梓（非管理科学专业）

    （4）朱淑媛、张瑞、杨海慈（非管理科学专业）

附：一等奖论文摘要

Dynamics of Complex Network in Information Dissemination

冯业倩、张唯佳、张众

Information spreading to exert influence is still considered to be of great significance for human prosperity. We apply both the complex network and dynamic system perspectives to model the information network in the past, present and future.

For task 1, we use 2 sets of models: WS&BA models in complex network field, and time-delay dynamic SIS, revised SIR and high-dimensional SIR models derived from epidemic model in dynamic system field, to analyze the features of the information network in 5 historical periods. Methods like fuzzy evaluation, time series analysis, phase portraits and numeric experiments have been applied to analyze the role of network connectivity and information inherent value in the information dissemination. Additionally, news is defined considering the Pulitzer rules to be “aimed at affecting more information agents by truth”.

For Task 2, we collect the historical data and calculate the information inherent value. Using the inherent value and other arguments for network structure, we simulate the information spreading to show propagation scope and time of data we collected. We apply theory of “Three degree of Influence” to the improved model for better fitting degree to reality. The effectiveness of our model is also verified in this section.

For Task 3, 2 three-layer complex network models are derived from models in Task 1 to show more complex but structured information networks in 2050 from complex network and dynamic system perspectives. Structured network helps the information dissemination to be more efficient.

For Task 4, multi-agent simulation and 4-dimentional SI derived model are used to analyze how people change their opinions. Being convinced by authorities or crowd and interaction between different opinions stimulate people to change. We find inherent value of information, network connectivity, immune nodes and authorities important to influence change rate comprehensively.

For Task 5, combining the former results with Cobb-Douglass Production Function, we create our model to show the mechanics of information dissemination and public opinion transformation. Although inherent value and connectivity serve as main factors with different weight relevant to time, form and initial thoughts are also taken into account for more accurate estimation of information spreading and change in ideas.

Additionally, we conduct sensitivity analysis on complex network and stability analysis on dynamical system, verifying the reliability of our model.

Key words: Complex Network, Dynamic System, Information Dissemination, Information inherent value, network connectivity

Will we fail in the war of water resources?

刘之新、刘炫宇、熊慧梓

With the increase of the amount of countries and regions which are short of water resources, water scarcity is becoming a critical issue disturbing people all over the world. Being devoted to analyze an arid region, there are five issues to be dealt with.

l  Evaluate the water availability in the region.

l  Acquaint the factors causing the water scarcity.

l  Predict the water resources position in the future.

l  Adopt necessary solutions to solve the water scarcity in the region.

l  The impact caused by the solutions on the water scarcity.

In order to evaluate the water resources position from past to the future, we must design an appropriate model to realize the situation and predict the trend from the angle of supply-demand. In this section, firstly we are required to set up a function to estimate the water availability. And then, we pick up an arid region in China to evaluate the water scarcity by calculating the ability of development and utilization of water through DEA. The factors causing water scarcity also are analyzed by estimating the rainfall and sewage. At last, we use the multiply regression analysis to predict the water situation in the future in the region.

Not only have we evaluated the position, but also we devote ourselves to tackle the problem of water scarcity. We hammer at promoting the water replenishment by purifying contaminated water. Exactly speaking, we suppose to build the sewage treatment plants and measure the long-term influence on the region as well as its surroundings. The facilities’ efficiency is assessed through profit-cost analysis. Last but not least, we test whether the sewage treatment plants that are applied in the region we picked up are beneficial for solving the water scarcity.

Key words: System Dynamics, DEA, Multiple Regression Analysis  

朱淑媛、张瑞、杨海慈

Firstly, we construct a model of information transmission network based on the social community network. The social network model is composed of two layers, the first layer is the multi-center model which describe the relationship between media; the second layer is a network model with small world properties designed for the interaction between individual nodes. Based on the social network, we introduce the SIR model to make the rules of information dissemination on social network so as to obtain an information flow network. Besides, we assume that the condition for a message to be delivered is that the intrinsic value of the message is greater than the cost of the transmission and the value of information is determined by the time, region and content. By analyzing the characteristics of  the five periods, we obtain the social network topology structure and information campaign strategy corresponding to each period. Ultimately, we redefine the news by using the results of Monte Carlo simulation.

After the model is established, we test the reliability and predictability of the model. Firstly, we select3 typical events from different periods. After setting the initial value of the event, we use the model to calculate the end state of the event propagation. Comparing the results with stories after that event, we get to conclude that the results of the model are consistent with the reality of the past and the model is proved to be effective . To evaluate the prediction capability, we analyze of data and its trends and put predicted parameters into the calculation model. The results show that the relationship and capacity of the modern information transmission network derived from the model are quite equivalent to today's actual value, which proves that the model has a strong predictive ability. Then we use the same method, combined our understanding of the information age, make a prediction for 2050. The result shows that the information penetration rate in 2050 will be higher, but the entire information environment will be more orderly.

李雪阳、丁方洁、刘馨儿

For task (a), in order to explore the flow of information based on 5 periods, we develop an Average Speed of Year (ASY) model according to the proportion of media people use to get information. The ASY model reflects the change of the deliver speed of information according the time of year. Then we develop an Influence Value of Information(IVI)model to evaluate the inherent value of information, thus figuring out what qualifies as news on the basis of information’s influence value.

For task (b) and task (c),with ASY model, we come up with the change curve of information speed in history, which fits the development of technology. Then, we predict the proportion of media and the information speed of 2016 and 2050, which proves the limited prediction capability of our model. Meanwhile, we use IVI model to distinguish news from other kinds of information from the data of Sina Microblog.

For task (d), based on the fundamental SIR model, we establish an improved model of how public opinion transmits and changes through information networks. Firstly, we see the whole network as a directed graph G(V,E) where V is the set of nodes which represents people in the network and E is the set of directed edges which information passes through. According the SIR model, we figure out how node’s position (susceptible, infectious and removal) will change. Secondly we apply Basic Deffuant model to improve our model, taking the opinion of nodes (the degree of support, neutrality and opposition) into consideration.

For task (e),we have read some papers about the task. Information value is restricted by objective and subjective elements which influence the spread of information and the public opinion. One’s opinion is affected by views of people around him, and all the individuals’ opinions in a system combine to form the public opinion. The form of message or its source impact how information spreads and how people receive it. The topology of the information network in a certain area could help in the design of information acquisition systems and thus accelerating information spreading process.