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我们的参赛队号为：1287

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参赛队员(签名) ：

队员1：赵磊

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数学建模国际赛

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竞赛评阅编号（由竞赛评委团评阅前进行编号）：

Can Science Solve Terrorism?

Abstract:

Today's world terrorism threatens the security of the whole mankind. Compared with the black society, the harm to the state and society is much greater. It not only has the organization and the system, but also because of the political purpose. It leads to the extreme and the madness. We need to do a good job, that is, we need to understand the behavior of the relevant objects (the type of network resources used to use the type) of its risk index (psychological characteristics) to evaluate and classify by scientific methods.

For task 1, we believe that the data can be used to predict the behavior of the research object, and then predict the risk index, so the network resource type is used as the forecast factor. The BP neural network model, which is established by us, is chosen as the input layer, and the risk index weighted total cooperation is the output layer.

For task 2, a large amount of data is obtained by a large number of monitoring data, and the risk prediction model of the BP neural network is used to predict the risk index. We have data which type is unknown . We can use K means SPSS to classify data by analyzing the clustering method based on our risk index.

For task 3, we can determine the risk index of the object by using the model we established. We can also carry out a large number of monitoring data, so that we can effectively find and monitor the risk index. Based on the above analysis process, conclusion and the current situation of the social objective for Obama to develop relevant and effective containment measures for ISIS.

Key words: BP neural network model K neural network model means-clustering algorithm Psychology Terrorism

Contents

1. Introduction (3)

1.1 Why does toll way collects toll? (3)

1.2 Toll modes (3)

1.3 Toll collection methods (3)

1.4 Annoyance in toll plazas (3)

1.5 The origin of the toll way problem (3)

1.6 Queuing theory (4)

2. The Description of Problem (5)

2.1 How do we approximate the whole course of ? (5)

2.2 How do we define the optimal configuration? (5)

2.2.1 From the perspective of (5)

2.2.2 From the perspective of the (6)

2.2.3 Compromise (6)

2.3 Overall optimization and local optimization (6)

2.4 The differences in weights and sizes of (7)

2.5 What if there is no data available? (7)

3. Models (7)

3.1 Basic Model (7)

3.1.1 Symbols and Definitions (7)

3.1.2 Assumptions (8)

3.1.3 The Foundation of Model (9)

3.1.4 Solution and Result (11)

3.1.5 Analysis of the Result (11)

3.1.6 Strength and Weakness (13)

3.2 Improved Model (14)

3.2.1 Extra Symbols (14)

3.2.2 Additional Assumptions (14)

3.2.3 The Foundation of Model (14)

3.2.4 Solution and Result (15)

3.2.5 Analysis of the Result (18)

3.2.6 Strength and Weakness (19)

4. Conclusions (19)

4.1 Conclusio ns of the problem (19)

4.2 Methods used in our models (19)

4.3 Application of our models (19)

5. Future Work (19)

5.1 Another model (19)

5.2 Another layout of (23)

5.3 The newly- adopted methods (23)

6.References (23)

7.Appendix (23)

Programs and codes (24)

I. Introduction

1.1 Task 1

Today's world terrorism threatens the security of the whole mankind. It is harmful to the state and society. It not only has the organization and the system, but also have political purpose. It has caused the extreme and the madness. Terrorism affects the security of the neighboring countries and the national peace and social unrest, which greatly hinders the economic development and social progress, and the political unrest, social unrest, the destruction of world peace and development.

1.2 Task 2

The existence of terrorist organizations and the growth of modern high-tech weapons, in addition to, the most important is the organization of the human (new force) and the corresponding activities. Modern behavioral psychology has proved that people's awareness of the activity is active, it is a purpose, there are plans to carry out. That is to say, the behavior of people and their characteristics are the external objective of psychological characteristics, through some behavior or habits of people, we can do their corresponding physiological characteristics of their psychological judgments, so as to analyze their future behavior.

Now network technology and the development of large data and developed so that we can use some people use different kinds of network resources and their tendency to use data to establish mathematical model, and then analyzes the psychological characteristics of people, and through the analysis of relevant as possible to avoid and prevent some correlative tendency people go astray, reduce the staff strength of terrorism. It is necessary to solve the problem of terrorism in all countries and regions.

1.3 Task 3

Today's world terrorism threatens the security of the whole mankind. It is harmful to the state and society. We should take a scientific approach to the terrorist organization like IS.

II. The Description of the Problem

2.1 Task 1

The so-called risk assessment is through certain techniques of certain objects terrorism tendency to judge the possibility, which provide the basis for controlling the risk.

Prevailing international risk assessment tool on crime reference point of view, the basic principles of risk assessment and technology mainly in the development and use of prediction on the table, that is, selection factors may be associated with terrorism through investigation and experimental research, the use of appropriate mathematical

model for statistical processing, so that the possibility of presumed tendency of terrorism size. Risk prediction generally through the following links.

(A) Collect information

According to the task that we can adopt the outlook law, that for a prediction target, within a certain time frame prediction, and risk analysis related to predictors of thought, in whole or in focus by the survey were collected.

(B) Select predictors

The key risk prediction is a predictor of choice. First, I want to get the information, select and terrorism tend to have significant relationship factors as an alternative predictors. Secondly, the use of BP neural networks, fuzzy mathematical model established mathematical calculation of the various factors related to the degree associated with terrorism, as the choice of standards. In order to predict the ease of operation, the number of predictors should not be too much.

According to the current characteristics of psychology point of view by browsing the network resource types. We determine the following factors of risk assessment predictors. Military news, political news, games, entertainment, science and technology, culture, welfare, illegal harmful information are included.

(C) Predict the number of factors (weights) of

For several predictors selected, based on their degree of correlation with terrorism tends to be given appropriate weight.

(D) Risk preliminary forecast

Obtained by calculating the weighted sum of the total score, the score is made to the number of psychology and terrorism tendency risk prediction, as an effective tool to predict terrorism.

Critical interpretation of scores in the risk assessment for. The resulting total score by specifically explain the tendency to judge the size of terrorism

2.2 Task 2

The task is to develop a series of effective and fast automatic classification method through a large number of monitoring data. The risk prediction model of the BP neural network is obviously effective and fast automatic.

We know that the so-called clustering, is to put a large number of D dimension objects (n) into k clustering (k

Task two is roughly such a problem, we have data but the data category is unknown, through the analysis of our data based on the classification criteria of the risk index to cluster analysis, this situation using K means - SPSS clustering method is appropriate.

2.3 Task 3

According to the above tasks one and two we can monitor the use of various types of network resources by the model we established. We can determine the risk index of terrorism. It can also be a lot of monitoring data for the rapid and effective classification.

The use of this model requires a long-term investment, so as to avoid each time only when the crisis comes to the development of a variety of policy. Based on the current situation, it is sure to have a big project like Manhattan plan to understand the behavior of terrorists, and continue to invest in more psychological research and the analysis of the mathematical model of a clear numerical analysis. Psychology has great potential to make us understand terrorism, and to provide a policy system to reduce the behavior of terrorism.

Obama's recommendations should be based on the above analysis process about terrorism, conclusions and current social objective conditions, and the practice of ISIS should be based on the above mentioned above to the corresponding specified effective measures to curb.

III. Models

Assume we can monitor some people's Internet use. We didn't know what people were looking at on the internet (for example, depressed person - a dead giveaway), but merely how they were using the internet. None of the data categories gave specific information about what websites people were visiting, the content of their emails or chats, or the types of files being downloaded – we simply indicated the extent to which people used different broad categories of net-based resources, as well as differences in people's tendency to use many resources at once.

Symbol Description:

Symbol Description

1 Wij the weight of each layer is generally

between [0,1] value

training sample

2

X=()

the desired output

3

Y=()

4 The output of i neurons in k layer

5 The self-learning error of i neurons in k

layer

6 threshold

7 B threshold neuron

8 E A data set of all objects and squared error

9 P An object

10 m i Ci cluster centroid

11 d(Vi,Cj) Distance

12 O computational complexity

13 t The number of cycles

3.1 Task 1

3.1.1 Basic Model

We believe that the data can be predicted through the network resource, so we should use the network resources as a predictor, so we set up the BP neural network model selected military news, political news, games, entertainment, science and technology, culture, public interest, harmful illegal information, and set 8 hidden layer variables, and risk index weighted total cooperation as the output layer, the specific modeling see below.

(A)Basic theory of neural modeling

BP neural network is also called the error back propagation network. BP network has good tolerance, and the contribution to the network is limited. In the process of learning, it has the advantages of strong immunity, and it has strong applicability. It is widely used in the fields of speech recognition, industrial process control, credit evaluation and stock forecast, and the results are quite accurate. BP network is the most mature artificial neural network.

BP network is the error of the back propagation, and constantly correct weights and thresholds, so that the error is close to or achieve the desired level. The decrease of the error is usually used in the negative gradient descent method. BP network is essentially a high accuracy numerical fitting. Its principle is to motivate function together. It achieves the purpose of error as small as possible by changing the coefficients of each excitation function.

(B)The establishment and solution of the model

Algorithm description of BP neural network:

(1) The weight of each layer of the value initialized. Network weights generally

between [0,1] value.

(2) Pre-processing the input data, providing training samples and the target output. Input sample: X=()

Output: Y=()

(3) Calculate the output layers

For the first layer of its k neurons output are:

(4) The learning error of each layer is , and the output layer is k=m, there is:

For the other layers:

(5) Correction weight coefficient and thresholds:

(is the learning rate)

(6) When the weight coefficient of each layer is calculated, it can be determined whether the given quality index is satisfied. If the request is satisfied, the algorithm ends; if not satisfied, it returns (3).

(C) In the risk assessment process BP neural network program

In the terrorism risk index for assessing tendencies, due to the large number of samples and terrorism tendency in practice and selection of military news, political news, games, entertainment, science and technology, culture, welfare, illegal harmful information several predictors correspondence is not entirely certain, there could be arguments are the same as above.But the risk index of different circumstances, then the study of computer neural network may have a huge misunderstanding, so the number of training in the model is 8, learning speed is 0.0001. Using the premnmx function to normalize the operation in order to make the neural network have good ability to speculate.

Fig. 1. Schematic diagram of BP neural network

The network structure is used as the conventional three layer network structure (8 hidden layer nodes), as shown in the following diagram: input layer, middle layer (hidden layer) and output layer. The upper and lower layers are fully connected, but the same layer of neurons are not connected. The input neurons and the hidden layer are the weights of the network. Hidden layer and output layer either neuronal integration of all neurons in the previous layer of information, in the integrated information to add a que value. This is mainly imitate biological neurons must reach certain que will trigger the principle of value, and the integration of information as the input neurons. When a pair of learning samples are provided to input neurons, the neuron's activation value (the layer neuron output value) is transmitted from the input layer to the output layer. The input response is obtained from the input layer of the output layer. Then the input layer is inverted from the output layer to the input layer.

As this error reverse propagation correction is repeated, the correct response rate of the network input mode is also rising. BP algorithm is the mathematical core of the "negative gradient down" theory that error reorientation BP network is always the fastest decline in the direction error.The three-layer BP network weights and threshold adjustment formula is as follows:

E: error square network output a nd the actual output sample between and; η: learning rate, that is network weights adjustment; : t time the i-th input layer and the

: time

hidden layer neuron j-th the connection weights of neurons;

i-th input layer neurons and the connection weights j-th hidden layer neurons; :

in the hidden layer of the j neurons and the output layer of the K neurons in the connection weights; : k-th connection weights hidden layer neurons

moment the j-th neuron and the output layer; B : threshold neuron, the same sense of meaning and weight of the subject. The above four type is the BP network learning rules.

3.1.2 Analysis of results

For the test of the model, the risk index of the actual tendency of human terrorism is obtained, and the risk index of the network output is compared with the network output risk index and the network training results are shown in Fig.2.

Fig. https://www.sodocs.net/doc/5a17273246.html,parison between actual risk index and network output risk index

Fig. https://www.sodocs.net/doc/5a17273246.html,work training results

Figure 3 shows that the error of the network training is very small, and the target value is reached. Figure 2 is a comparison between training and testing of the actual sample and network output values. It is clear that the two are very close and the error is small, so it can be assured to predict. Here is the case of the case because the sample number is relatively small, the test stage used the training sample. Research object data are substituted into the established neural network model, the research object of the terrorism risk index, as shown in the diagram below.

Fig. 4.Risk index for predicting the risk of terrorism

According to the establishment of the model, substituting the data to solve and according to many were square error calculation of the revised calculated error is small and the actual data is roughly consistent with the weighted sum, a measure of the fraction of 0 - 100 points. According to the risk index and the analysis of the tendency of terrorism, the target object is evaluated.

Score Terrorism tendency

0—20 ·

21—40 ··

41—60 ···

61—80 ····

81—100 ·····

For weighted aggregate scores in more than 60 points with highly, highly inclination objects should be to focus on and understand the current behavior, psychological state determines that the judgment is true. If it is true, we should correct orientation in psychological, prevent it to terrorism or let it come out from the shallow terrorism, and use scientific methods to solve the terrorism.

3.2 Task 2

3.2.1 Basic Model

The task is to develop a series of effective and fast automatic classification method through a large number of monitoring data. The risk prediction model of the BP neural network is obviously effective and fast automatic.

We know that the so-called clustering, is to put a large number of D dimension data objects (n) into k clustering (k

Task two would roughly be such a problem, we have the data, but data type is unknown, cluster analysis by analyzing the data we have our risk index based on classification criteria. Facing this situation, we choose to use clustering method of

K-means of SPSS more appropriate.

k- means algorithm firstly randomly selected k objects, each object represents a cluster of center of mass. For the rest of the each object, according to the object with the clustering of the distance between the center of mass, it is assigned to the most similar with the clustering. The new then calculate every clustering center of mass. Repeat the process until the convergence criterion function. Usually USES the criterion function is the squared error criterion function (squared-errorcriterion):

E is a data set error sum of squares of all objects, P is an object, mi is the center of mass cluster Ci:

k-means clustering algorithm of the specific steps are as follows: (1) from the data set selection K centroid C1, C2,... , Ck as the initial clustering center, and the most similar to each object assigned to the polymerization. Each aggregate is represented by means of which all objects are represented, and the "most similar" is the minimum distance. For each vertex VI is to identify a centroid CJ, make it with a distance between D (VI, CJ) minimum, and the VI is assigned to the group; (3) to all points are assigned to the corresponding group after the re calculation of each group centroid CJ; cyclic execution the step 2 and step 3, until the data partition doesn't change. The algorithm has a good scalability, and its computational complexity is O(nkt). t is the number of cycles. The task needs to solve and explain according to the establishment of the model, substituting the data to solve the large data set will be fast and efficient automated classified into one of five types of tasks, and thus focus on the object height, the height of terrorism The crowd tends to be monitored and appropriate measures. Results obtained are as follows K-means:

3.2.2 Analysis of results

According to the above model, substituting the data obtained in Figure 5, the initial cluster center：

Fig. 5. Initial clustering center

The final clustering center is obtained by the clustering algorithm, as shown in Figure 6：

Fig. 6. Final cluster center

The collection of large data is automatically classified into 5 categories (from 1 to 5 terrorist tendency from high to low) and the number of each category is statistically. K - means results are as follows:

Fig. 7.Number of various categories

3.3 Task 3

For this problem, we need a long-term investment, so as to avoid a time when the crisis came frantically to develop policies. We need a big project to understand the behavior of the terrorists, and continue to invest more funds to carry out psychological research. Only in this way can we go beyond now use "folk psychology" to explain the phenomenon we encountered state. Psychology has great potential to let us know of terrorism and their strategy system. Indeed, the concept of psychology is increasingly being abused by other subjects in the absence of a clear context or restrictions, especially in Political Science. Even so, the first question always concerned with psychology when a crisis occurs- why and how a person become a terrorist? If we can stop it from happening, how to do it? What measures should be taken to ISIS?

Based on the psychology, we could set up the risk coefficient of the monitored object by monitoring the use of network. For a large number of monitoring data, the government should promptly to the high risk of the people from various aspects of in-depth investigation to understand. We should invest them from many aspects to assess. Such as the people's work unit, family situation, cultural level, religious belief, political faction, criminal history and so on. If this person does have a tendency to commit terrorist crime, it should be timely to conduct a criminal psychological treatment, such as the use of the principles and methods of psychology, mental health education, psychological counseling and psychological treatment, psychological prediction and crisis intervention and a series of activities. Criminal psychological correction can be carried out from the following five aspects.

First, to enhance the thoughts of terrorism tendency of understanding level. We can strive to improve their legal and moral cognitive abilities, and make them understanding their own mental and behavioral problems so that we can fully aware of the causes of social nature of their behavior generated and find the right way to treat them, raising the level of thinking and understanding. We help them to eliminate unhealthy psychological and other psychological barriers, maintain and restore mental balance, promote mental health, and enhance the adaptability of life, in order to eliminate the tendency of violence and terrorism.

The most important is to carry out legal education to help them understand the law in real life and the necessity of the use of the law, we can educate that they can not violate the law when dealing with relationships with others in society. The most important thing is that we shall not do harm to society and public security. Second, to divert the people's negative emotions. Criminal psychology research shows that the accumulation of negative emotions tend to be important factors lead to the crime of terrorism, They may show the situation of crime of passion Under the stimulation of accidental events when the cumulative to a certain degree of negative emotions beyond the limits of the crime. So, trying to allay their fears, tension, anxiety, depression, despair, resentment, anger, pain and pessimism and other negative emotions, to facilitate their emotional balance, to form a good emotional

reaction mode and maintain a positive emotional state is an important step.

Third, to help these people change their cognitive structure and thinking mode. The important reason of the tendency of terrorism is that they do not deal with the problems and contradictions well in the social life, especially when it is in social life. The one-sidedness of cognitive or thinking and easy to over-emphasis on certain contradictions are the reasons that they do not properly deal with the problem. They will make them re-establish the correct attitude to oneself, to others, to society, to raise awareness ability, to develop the right mindset, to make them the right, to treat various problems encountered in daily life by treatment activities.

Fourth, to develop their self-control ability. Although they understand legal norms and have the right and wrong would make the wrong behavior when the individual's self-control is low and the right idea with a strong personal desire conflict. People with low self-control tend to be driven by impulse, so that they can act as a restraint on social norms. Therefore, cultivating their self-control ability in order that they can actively adjust their mental state and behavior, when confronted with severe mental stimulation, they will not produce impulsive behavior and will be possible to effectively control crime in the face of external stimuli or incentives own. They do not make criminal terrorist behavior. They may be in the face of external stimuli or crime inducements to effective control of their own, not as a result of the impulse to make illegal and criminal acts of terrorism.

Fifth, to correct their bad habits. The formation of criminal psychology is usually a process, often by criminal acts against public order, public property, relationships, social groups, family relationships, lifestyle and other aspects of unethical or illegal habit minor development. Therefore, an important work of psychological treatment is to correct their presence of various behavior, develop their behavioral responses to form a good pattern, and enhance their ability to adapt to various situations behavior. Help them build good relationships.

In addition, it is also a long time for these people to monitor, to correct the initiation of the idea of terrorism. For ISIS, such an extreme terrorist groups, if necessary, can be expanded air force means, such as armed combat. let IS the terrorists know, justice in the world has never been stopped fighting their footsteps.

IV. The model of evaluation, improvement and popularization

4.1 Evaluation of the model

By solving the above problems, we use criminal psychology, BP neural network model, clustering analysis method and other knowledge and methods to establish the risk index and the fast classification of large data through known data:

(1) Determine the risk index of the target (the use of different types of network resources in the use of the data)

(2) Automatic classification of large data

Through the BP neural network to establish the risk index model, it can be more accurate to predict their psychological, and then judge the tendency of its terrorism. Clustering fast classification model can be selected according to different needs. And input corresponding data, which be classification.

However, because the establishment of the first model is the ideal model, ignoring the impact of the role of each factor in the prediction of psychological prediction is objective statistical conclusions, there is a certain applicability, but not necessarily suitable for all data and objects, so the results are approximate results. There are errors can only be used for roughly forecast, the specific judgment or need to be investigated to understand. The inadequacies of the second model of K - means clustering algorithm is it must repeatedly scan the database. In addition, it can only find out the spherical class, and not found class of arbitrary shape. Also, the selection of the initial center of mass has a greater impact on the clustering results, which is sensitive to the noise.

4.2 Improved methods for models

4.2.1 Improvement of task 1 model

(1) there is a question of accuracy and operability of the data

We do not fully understand the behavior and psychological characteristics of people who really have the tendency of terrorism, and it is difficult to operate. So the accuracy of the forecast factors is not entirely accurate. The results may be more accurate. These results may have some errors.

(2) algorithm problem of model

BP neural network model of learning and parameters according to different types of prediction factors of their learning style is also very different, learning methods need to be corrected according to the prediction factor.

4.2.2 Improvement of task 2 model

The clustering results of K-means algorithm are sensitive to the initial center, and the K value can not be determined. In view of the above shortcomings, we can correct the algorithm. The algorithm is sorted by the distance and the data set is divided into K group by calculating the distance of each data point to the origin of the data set. Then the data points in each group are selected as the initial center. The time complexity of the algorithm can be greatly reduced by optimizing the operation of the data distribution to each cluster.

4.2.2 Improvement of task 3 model

The model can be used to modify the input layer and the prediction factor, which can be used in the field of criminal justice, and it can be used to predict the behavior. Model 2 K-means algorithm clustering algorithm is a classical algorithm can be used for large data mining processing, for a variety of large data classification, customer segmentation, and so on, has great application prospects and effects.

VI. References

[1], Ma AI Zhang Enyou, criminal psychology, Beijing: Renmin University of China press, 2015.

[2] Liu Qi et al., criminal psychology, Beijing: Chinese People's Public Security University press, 2006.

[3] Sui Shulin, etc., mathematical modeling tutorial, Beijing: Chemical Industry Press, 2015.

VII. Appendix