Depression is famous for its capacity to make devastating impact on people’s physical and mental well-being and sense of happiness. Many researches have tried to identify different factors that function on different groups of people. In this research, the method Binary Logistic Model is used to deal with the data from a study about the life condition of people in rural zones, and was first published online in 2019 and compiled in 2020, with 1429 individuals as its samples. It is concluded that although depression has no connection with sex, marriage, number of children, members in family, gained asset, durable asset, saved asset, living expenses, other expenses, income from salary, income from farm, income from business, income from non-business, income from agriculture, farm expenses, labor primary, lasting investment, non-lasting investment, it has a relatively strong connection with age and education level. This paper focuses on people in rural zones, and concerns 20 factors that cover many aspects of their lives simultaneously, which hopes to help further study of depression.

This article mainly talks about the differences in the calculation method of rating deviation (RD) between the Glicko and Glicko-2 systems and how they affect the player’s rating differently. In addition, it also includes the logician of the Glicko-2 and how it operates in real situation. In Glicko-2, the change of RD is based on more information contained in one match unlike Glicko which is just based on the play counts. In addition, the Glicko-2 solves some problems presented in the Glicko and gives players better game experience, and rationalizes the player’s data, makes an improvement of Glicko. This article includes detailed explanations, by using some examples and figures of functions, illustrate the relationship between RD and the difference of rating, opponent’s RD, and the player’s RD itself, also give some examples of how the mechanism of calculating RD is used in other cases, like the game Tetr.io. Thus, this paper underscores the importance of new ideas in the Glicko-2 system.

As the stock market plays a crucial role in the world economy, researchers have used multiple mathematical and statistical models such as Artificial Neural Networks (ANN) and Long Short-Term Memory (LSTM) networks model to forecast the fluctuation in stock price despite their unpredictability as the stock market, being a stochastic process, would be easily affected by an abundance of factors such as governmental policies, industrial news, and natural calamities. Therefore, based on the previous studies, this paper attempts to forecast the stock opening price of Apple Inc., one of the world-leading companies in the technology industry, utilizing the Autoregressive Integrated Moving Average (ARIMA) model. In order to minimize the impact on the stock market brought by the COVID-19 pandemic, this paper will analyze separately the opening price of Apple stock before and after the epidemic outbreak and will compare the difference the pandemic made in the stock market, as well as the forecasting models.

Studying music from a mathematical perspective is often based on the notions of symmetry and topological space. A group G acting on some set S of musical objects in a meaningful way is seen as a symmetry group in music. This can be used in analysing motif development and chord progressions. In neo-Riemannian analysis, one has three principal chord transformations that generate a group G≅D_12, acting on the set S of 24 major and minor triads. Moreover, this theory is visualized through a simplicial complex whose underlying space is a topological torus. In this paper, we first introduce various symmetry groups and graphic presentations in music theory. We then propose a way of doing neo-Riemannian analysis on Klein’s quartic, which is a genus 3 surface instead of a torus, realizing an idea of John Baez. Finally, we use our theory to perform a harmonic analysis of The Imperial March from “Star Wars”.

Maximum likelihood estimation is a breakthrough in the history of statistics, which overcomes the main weakness of Bayesian estimation and has been widely used in various fields, such as language and image processing, and system identification, etc. This paper analyzes the application of maximum likelihood estimation on different mathematical models. It is proved that the universality of maximum likelihood estimation plays an important role in promoting the continued in-depth research on maximum likelihood estimation. This paper also analyzes and summarizes the application of maximum likelihood estimation to specific parameters in different mathematical models. In addition, this work conducts research on the application conditions of maximum likelihood estimation and its main properties, such as variability, consistency, and asymptotic normality, etc. In different mathematical models, such as the annealing furnace efficiency system, gamma environmental factors and adaptive algorithm, etc. Therefore, this paper finds the reason for why the maximum likelihood estimate is widely used in various fields.

For the past 60 years, the number of silicon transistors — the building blocks of integrated circuits — that can be packed onto a microchip has doubled every two years. This phenomenon, famously termed Moore’s Law, has driven technological progress. However, this trajectory is approaching a barrier known as the “Silicon limit.” At sizes below a certain threshold, the efficiency of silicon diminishes, posing a challenge to continued miniaturization. Thus, the development of novel transistor materials has become a critical step towards realizing ‘beyond-silicon nano-electronics’. Graphene, a two-dimensional material composed of carbon atoms arranged in a hexagonal lattice, has risen to prominence as a potential way forward in the field of nano-electronic devices due to its numerous advantages, including high electron and hole mobilities, an atom-thin structure, and the ease of doping to enhance conductivity. However, the lack of a band gap in graphene poses a significant challenge in designing efficient nano-electronic devices. While cutting graphene into nanoribbons can open a band gap, further scaling down graphene nanoribbons will be difficult and costly. Therefore, alternative approaches to further enlarging the band gap based on the current size scale are essential. In this study, we propose a novel method to successfully increase the band gap of 7-armchair nanoribbons by introducing the pre-designed shape of cutting. Additionally, by further manipulating the cutting shape, we also propose a method to increase carrier’s mobility while retaining the band gap. These findings represent a significant advancement in optimizing the electrical performance of future carbon-based transistors. The utilization of pre-designed cutting shapes offers a flexible approach to tailor device performance according to specific requirements, thereby enhancing the versatility and functionality of carbon-based electronic devices.

In recent years, the student-teacher ratio (STR) has received widespread attention in the field of education. By now, the STR has become an important indicator of education. This article first theoretically analyzes the relationship between the STR and the proportion of the school-age population in the middle school stage to the total population of the country, teacher gender ratio, the proportion of education expenditure in GDP, and GDP per capita, predicting that there is a positive correlation between STR and the proportion of school-age population in the total population, and there is a negative correlation between STR and the rate of women teacher, the proportion of education funds in GDP, and GDP per capita. Then this article establishes the regression equation of STR and the above variables through the data of secondary schools in China in the past 30 years. And it finds that there is a positive correlation between STR and the proportion of the school-age population in the middle school stage to the total population of the country, and there is a negative correlation between STR and the rate of women teachers, and GDP per capita, and there is no linear relation between STR and the proportion of education funds in GDP. Also, this article finds that proportion of the proportion of the school-age population in the middle school stage to the total population of the country, rate of women teachers and GDP per capita have collinearity relationship.

This study delves into predicting song popularity on Spotify by analyzing a dataset of song features from 1986 to 2022. Using linear regression, this paper examines the influence of audio characteristics such as energy, danceability, speechiness, duration, and mode, alongside the year of release. The findings indicate that danceability, more recent release years, and longer track duration are positively associated with higher popularity levels. Conversely, songs in minor keys are more favored than those in major keys. These results highlight the significance of both intrinsic musical qualities and evolving listener preferences over time. The model's robustness is ensured through comprehensive diagnostic tests that validate the assumptions of linearity, normality, and homoscedasticity, confirming the predictive reliability of the identified factors. This research not only enhances the understanding of the dynamics driving music popularity but also provides valuable insights for artists and producers aiming to optimize their music for digital platforms. By focusing on the critical elements that resonate with contemporary audiences, stakeholders can better strategize their music releases to maximize listener engagement and success on streaming platforms.

In case of train delays, centralized traffic control system become disabled, and the workload of dispatchers increases dramatically. Based on genetic algorithm, the author designs a program to appropriately reschedule trains in terms of delays, minimizing the total delay time and changes of gate. The author transformed the initial problem to a compromised combinatorial optimization model, with total delay time, changes of gate and conflicting routes as objectives. The high weighting in conflicting routes ensures efficiency and high probability of obtaining a feasible solution. With discreate variants, the author designs special coding and evolving method suitable for this problem. Using a special treatment for conflicts and initializing chromosomes, the program can construct new timetable quickly given the scheduled timetable, predicted arrival time and order of trains (optional), which promotes the efficiency and security of dispatching in high-speed railway stations. The method was tested with a synthetic data of Shanghai-Kunming section of Hangzhou East Railway Station.

This paper introduces the basic theory and formula of linear regression, multiple linear regression, and nonlinear regression. Linear regression is one of the commonly used analysis methods in statistical analysis, which can predict the trend of model data change to a certain extent. Multiple linear regression involves more variables to predict and analyze the change trend of data, and can predict the change of data more accurately. Nonlinear regression can predict the model of arbitrary relationship between variables, thus obtaining more accurate prediction data. In the selection of regression analysis method, data characteristics and problem background should be considered, and model assumptions and validation should be paid attention to ensure accuracy and reliability. In the applications, the paper discusses the application of simple linear regression to Okun’s law and delves into the complex relationship between multiple variables and gross domestic product (GDP). Finally, it uses nonlinear regression equations to analyze the global inflation rate and the annual data, and proves that there is a nonlinear relationship between the two and a downward trend, which is supported by analyzing the data of Australia and Canada.