Urgently looking for the translation of 2012 American Mathematical Modeling Question C!

Crime Solving Model

Your organization, ICM, is investigating a conspiracy. Investigators are very confident because they know several members of the cabal, but they hope to identify other members and leaders before making arrests. The mastermind and all possible alleged co-conspirators worked in complex relationships for the same company in a large office. The company has been growing rapidly and made a name for itself developing and selling computer software for banks and credit card companies. ICM recently received information from a small group of 82 workers that they believe will help them identify the most likely candidates for currently unidentified conspirators and unknown leaders within the company. Since the flow of information involved all workers working at the company, it is likely that some (perhaps many) of the identified communicators in this flow of information were not actually involved in the conspiracy. In fact, they were sure they knew some people who were not part of the conspiracy.

The goal of the modeling effort was to determine who were the most likely co-conspirators in this complex office.

A priority list is ideal because ICM can investigate, select, and/or interrogate the most likely candidates based on this.

A dividing line dividing non-conspirators from co-conspirators would also be helpful so that the persons in each group could be clearly classified.

It would also be very helpful to the prosecutor's office if the leaders of the conspiracy could be named.

Before giving the data from the current situation to your crime modeling team, your supervisor gives you the following situation (called the Investigation EZ) from when she worked in another city several years ago case. She is very proud of her work on simple cases, and she says that this is a very small, simple example, but it can help you understand your tasks.

Her data are as follows:

The ten people she believed to be co-conspirators were Anne#, Bob, Carol, Dave*, Ellen, Fred, George*, Harry, Inez, and Jaye#. (* indicates previously known co-conspirators, # indicates previously known non-conspirators)

She has numbered the 28 message records of her case according to the themes on which her analysis was based.

Anne to Bob: Why are you late today? (1)

Bob to Carol: Damn Anne always looks at me. I'm not late. (1)

Carol to Dave: Anne and Bob quarreled again about Bob's lateness. (1)

Dave to Ellen: I want to see you this morning. When can you come? Bring the budget documents with you. (2)

Dave to Fred: I can see you anytime, anywhere today. Let me know when is better. Do I need to bring budget documents? (2)

Dave to George: I'll see you later --- there's a lot to talk about. I hope everyone else is ready. Get this right? Very important. (3)

Harry to George: You seem nervous. What's going on? Don't worry, our budget will be fine. (2) (4)

Inez to George: I am really tired today. What about you, how are you? (5)

Jaye to Inez: Not so good today (?). How about going to have lunch together today? (5)

Inez to Jaye: Fortunately everything was calm. I'm too exhausted to make lunch today.

Feel sorry! (5)

George to Dave: Come see me now! (3)

Jaye to Anne: Are you going to have lunch today? (5)

Dave to George: I can’t go, I’m going to see Fred now. (3)

George to Dave: Come to me after meeting him. (3)

Anne to Carol: Who will supervise Bob? He was idle all day long. (1)

Carol to Anne: Leave him alone. He worked very well with George and Dave. (1)

George to Dave: This is very important. Damn Fred. How is Ellen? (3)

Ellen to George: Have you talked to Dave? (3)

George to Ellen: Not yet. And you? (3)

Bob to Anne: I am not late. And you know I work during lunch time. (1)

Bob to Dave: Tell them I'm not late. You know me. (1)

Ellen to Carol: Contact Anne to arrange the budget meeting schedule for next week. Also, help me calm down George. (2)

Harry to Dave: Did you notice that George looked nervous/stressed again today? (4)

Dave to George: Damn Harry thinks you're nervous. Don't let him worry, lest he pry around. (4)

George to Harry: I just work too late and have some problems at home. Don't worry, I'm fine. (4)

Ellen to Harry: I forgot today’s meeting, what should I do? Fred will be there, and he knows the budget better than I do. (2)

Harry to Fred: I think next year’s budget will make some people very stressed. Maybe you should take a moment today to reassure everyone. (2) (4)

Fred to Harry: I think our budget is normal, and I don’t think anyone feels stressed. (2)

The communication record ends.

Your boss points out that she has only assigned and numbered 5 different message topics:

1) Bob's lateness,

2) Budget,

3) Important unknown issues, possibly conspiracy,

4) George’s pressure,

5) Lunch and other social issues.

As seen in the message encoding, some messages have two topics depending on the content.

Your supervisor analyzes the case by constructing a communication network based on communication links and message types. The figure below is a message network model. The code of the message type is marked on the network diagram.

Your supervisor said that in addition to the known co-conspirators George and Dave, based on her analysis, Ellen and Carol are also considered co-conspirators. And soon, Bob recognized that he was indeed involved, hoping to get a reduced sentence. The charges against Carol were later dropped.

Your boss is still pretty sure Inez was involved, but has never opened a case against her.

Your supervisor recommends that your team identify the guilty parties so that people like Inez will not slip through the crackdown and people like Carol will not be framed, thereby increasing the credibility of ICM and preventing people like Bob from being framed. A chance to get a reduced sentence.

Current case:

Your boss has structured the current situation into a network-like database, which has the same structure as above, but is larger in scope.

Investigators have several clues that point to a conspiracy to embezzle funds from the company and use online fraud to steal credit card funds from customers who did business with the company.

The small example of a simple case she shows you, only 10 people (nodes), 27 edges (messages), 5 topics, 1 suspicious/conspiracy topic, 2 confirmed criminals, 2 A known innocent person. So far, this new case has 83 nodes, 400 edges (some involving more than 1 topic), more than 21,000 words of message records, 15 topics (3 of which have been considered suspicious ), 7 known criminals, and 8 known innocents. These data are given in the attached spreadsheet files: names.xls, Topics.xls, Messages.xls.

names.xls contains the names of employees corresponding to key nodes in the office.

topics.xls contains the code names and short descriptions of 15 topics.

Due to security and privacy concerns, your team will not have a record of all direct messages.

messages.xls provides the node pair that transmits the message, and the topic of the message (there may be more than one topic, up to 3 topics).

In order to make the communication of information more intuitive and visual, Figure 2 provides a network model of employees and message links.

In this case, the subject of the message is no longer displayed as in Figure 1. Instead, the number of topics is given in the file Messages.xls and described in Topics.xls.

Requirement:

Requirement 1: So far, it is known that Jean, Alex, Elsie, Paul, Ulf, Yao, and Harvey are criminals, Darlene, Tran, Jia, Ellin, Gard, Chris, Paige, and Este are not criminals. Possible message topics are 7, 11 and 13. More information about topics is in Topics.xls.

Build a model and algorithm, sort the 83 nodes according to the likelihood that they are conspirators, and explain your models and indicators. Jerome, Delores, and Gretchen are senior managers at the company. It would be very beneficial if any of the three of them were involved in the conspiracy.

Request 2: The priority list will mysteriously change if new information informs us that topic 1 is also related to the conspiracy, and Chris is a conspiracy? (That is, two more clues)

Requirement 3: A powerful technology for obtaining and understanding text information similar to this message circulation network is called semantic network analysis; as artificial intelligence and computational linguistics methods, which provide a structure and enable reasoning processes about knowledge or language. Another computational linguistics related to natural language processing is text analysis.

In our case, explanation: If you have access to the original message, semantic and textual analysis of the context and content of the traffic can be useful in helping your team develop better models and office staff How helpful and reinforcing is the classification of ?

Have you ever used these features to improve your model based on the topic descriptions in the file Topics.xls?

Requirement 4: Your full report will ultimately be submitted to the prosecutor's office, so be sure to state your assumptions and methods in detail and clearly, but no longer than 20 pages. You may include your programs as attachments in separate files so that your paper does not exceed the page limit, but including these programs is not required. Your supervisor hopes that ICM will be the world's best agency for solving white-collar, high-tech conspiracy crimes, and that your approach will help solve important cases around the world, especially those with very high message traffic databases (which may have several Thousands of messages and millions of words).

She specifically asks you to discuss in your paper how deeper network, semantic, and textual analysis of messages can help your models and recommendations.

As part of your report to her, please explain the network modeling techniques you used, why they were used and how they can be used with any type of network database to identify, prioritize, and Network models for techniques that classify similar nodes, not just criminal conspiracy and message data. For example, given various images or chemical data that indicate the probability of infection and some infected nodes that have been identified, can your method be used to find infected or diseased cells in a biological network?