In numerous tennis matches, people have discovered that there exists a kind of momentum in tennis competitions. When this kind of momentum forms, the player occupying the momentum exhibits an almost overwhelming consecutive win in this set. To study this kind of momentum, this paper uses the tennis match data of Jeff Sackmann on GitHub. Firstly, it conducts an exploratory analysis on the data of the men's singles tennis match at Wimbledon, and uses the TOPSIS comprehensive evaluation model with critical weighting to score the performance of the momentum of the players in a game, obtaining the broken-line graph of the momentum performance score for each point of both players. Afterwards, the random forest machine learning model with particle swarm hyperparameter optimization is used to fit and predict the change of momentum, and the confusion matrix indicates that the accuracy rate reaches 93.3%. The fitting results show that the number of times the player breaks serve and the cumulative number of game wins have outstanding contributions to the player's momentum.
Sex ratios of sea lampreys vary in response to the external environment. In order to analyze sex ratio and its dependence on local conditions, we need to develop models that reflect the relationship between sex ratio and resource availability. In this paper, we establish a link between individual sex and the availability of larval food resources. Then, we extend the object of study from individuals to populations and express the dynamics of the sex ratio as a differential equation. We introduce other factors affecting the sex ratio to refine the relationship between reproductive rates and sex ratios. To better model the growth of the lamprey population, we developed a Gompertz model that initially approximates the growth rate of the exponential function. And the introduction of the Allee effect provides a more comprehensive view of population growth.
This paper focuses on word difficulty prediction and classification on the basis of capturing a year's word game data. Although Wordle was all the rage, recent tracking data shows that the Wordle popularity appears to be declining gradually, and the number of players has a downward trend. To promote the healthy development of Wordle and assist game developers in adjusting their game strategies in time, this paper establishes a word difficulty prediction model. Before Wordle difficulty prediction model is established, we preprocessed the data, rasterizing the area to be studied. In phase I, we introduced a PSO-LSTM prediction model and performed specific training, achieving an accuracy rate of over 85%. After coding the letters in “EERIE”, we successfully obtained the percentage of word “EERIE” on March 1,2023 will appear. The second phase uses hierarchical clustering analysis to subcategorize words by difficulty. The difficulty of words is then divided into five levels based on the folded graph of clustering coefficients derived from the elbow rule. Finally, this paper presents a model accuracy test and suggests the idea that this model can predict the data of serial relationship within the existence time and can be extended to the evaluation and weighted ranking under the influence of other factors.
The issue of light pollution has been arousing more and more attention on a global scale. Oceans and atmosphere on earth are seriously threatened by light pollution. In order to identify and assess the light pollution risk level of a location, this paper establishes a two-phase comprehensive environmental assessment model for regional light pollution. In phase I model, this paper selected 12 indicators from three aspects: source of light pollution, severity of pollution problem, and resource availability of pollution. Subsequently, the Logistic Regression model (LR) was utilized to obtain the models of the light pollution source and the resource availability of the treated pollution, and the regression model was developed through several significant tests. In phase II, this paper used Spearman correlation coefficient analysis to obtain 10 effective indicators that are highly correlated with the amount of light used. Then we used the comprehensive weighting method based on the Ana-lytic Hierarchy Process (AHP) and Entropy Weight Method (EWM) to give weight to 10 indicators, and finally we evaluated the risk of light pollution in four different types of locations based on the TOPSIS comprehensive evaluation method. Finally, the sensitivity analysis of the model is carried out, and the results show that our model has good stability and is very reliable.
The study of species population change is one of the most classic topics in biology. In this paper, we consider not only intra-race competition but also competition between two species. It is assumed that the resources in the environment are finite in this paper. Improved on the Logistic Population Growth Model from Malthusian model, we built the Competitive Hunter Model for trout and bass referring to the Lotka-Volterra Model. In this paper, we presented the assumptions of the model and analyzed the equilibrium points of the model in numerical analysis and the typical trajectories in phase planes in graphical analysis.
This paper considers how best strategies should be chosen to effectively mitigate light pollution situations in cities with different light pollution scenarios. Firstly, a mathematical programming model is used to analyze the light pollution characteristics of four typical areas: protected areas, rural communities, suburban communities and urban communities, and four states are abstracted. Subsequently, using reinforcement learning models, the four abstracted states are used as the state space of the intelligences, while promoting green building and eco-city design, rationalizing the layout and height of road lighting, and improving the performance of lighting equipment and lighting solutions as the three governance strategies, constitute the action space. Through continuous training it was concluded that areas with strong road and residential lighting, frequent night-time camping and other activities adopt the strategy of rationalizing the layout and height of road lighting; areas with dense night-time light sources, high light intensity and long duration adopt the strategy of promoting green architecture and eco-urban design. And areas with a high demand for night lighting, high air pollution index or large open areas adopt the conclusion of increasing lighting equipment and lighting solutions.
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