As the discipline of machine learning becomes more and more popular and algorithms for Multi-Armed Bandit (MAB) problems are used more and more frequently, how to choose the appropriate algorithms in contexts with different characteristics is an important topic. Therefore, this study compares the three algorithms by introducing the core connotation and advantages and disadvantages of the explore-then-commit algorithm, upper confidence bound algorithm, and thompson sampling algorithm, and gives the three algorithms' existing optimisation algorithms at the moment, which provides a reference to the selection of suitable algorithms. The Explore-Then-Commit (ETC) algorithm is simple, whereas the Upper Confidence Bound (UCB) algorithm optimises the interface between the exploring and exploitation phases of the ETC algorithm and thus performs relatively consistently, the Thompson sampling algorithm outperforms the first two algorithms in many cases as it naturally balances exploration and exploitation. ETC is suitable for static environments, and UCB is suitable for scenarios where there is continual exploration. However, as more data is available, regret must be reduced over time. decreases and scenarios where there is a need to reduce regret over time, and the Thompson sampling algorithm is suitable for highly uncertain environments.

Ocean circulation plays a key role in the global climate system and marine ecosystems. Accurate monitoring and modelling of ocean circulation not only contributes to an in-depth understanding of climate dynamics, but also has important applications in marine biodiversity conservation, shipping route optimization, and early warning of natural disasters (e.g., storm surges and tsunamis). With the rise of big data technologies, the volume of ocean circulation data has increased dramatically, and traditional analytical methods are difficult to cope with these complex datasets. The efficiency and accuracy of ocean circulation studies can be significantly improved by introducing big data analysis and visualisation techniques. This paper provides an overview of the application of big data analytics and visualisation methods in ocean circulation research, discusses various analysis techniques used to handle big data sets, evaluates their effectiveness, and looks at future trends and challenges in the field, future research will aim to further improve the accuracy and efficiency of ocean circulation data processing.

Amidst the current challenges facing Earth, such as resource scarcity, unsustainable population growth, and climate change, this paper explores the potential for interplanetary travel, specifically assessing the feasibility of reducing travel time from Earth to another habitable planet, Kepler-22b. By adopting the Python programming language to validate the feasibility of interplanetary travel between Earth and Kepler-22b, the research demonstrates that applying the time dilation theory has the possibility to reduce travel time significantly. The findings suggest that the spacecraft would need to approach the speed of light, with acceleration reaching approximately 200 m/s², which is 20 times greater than that of Earth’s gravity. Consequently, the time used in the spaceship can be 40% of the time taken on the Earth.

Applied mathematics aims to solve problems in various fields using mathematical methods, and it also plays an important role in wind power generation. This article introduces the fluid dynamics model and wind speed profile model established through mathematical modeling. These two models can deeply analyze the potential of wind energy and optimize the performance of turbines. By studying these models, we can further understand the operating mode and optimization space of wind energy, thereby promoting the development of wind energy technology. Improve power generation efficiency, understand its operating mode and optimization space, and promote the development of wind energy technology. Applied mathematics not only enhances the scientific design and implementation of wind power generation but also promotes the progress and sustainable development of renewable energy technology. This article points out that under the background of green energy, with the continuous deepening of data analysis and modeling technology, future wind power generation systems will be more efficient and reliable. Meanwhile, this article aims to make greater contributions to achieving global energy transition and addressing climate change, promoting the advancement and sustainable development of renewable energy technologies.

The role of stringed instruments in traditional music is of significant importance, with their vibrational characteristics exerting a direct effect on sound production and timbre alterations. This paper aims to mathematically analyze the vibration of a stringed instrument, such as the pipa, through the microelement method and the Fourier transform, to explore its sound generation mechanism and energy loss. The partial differential equations of the string vibration are derived in the ideal state and transformed into solvable ordinary differential equations using Fourier transform to obtain the analytical solutions for the displacement, velocity and acceleration of the string. In addition, the kinetic and potential energies of the string are investigated and an expression for the total energy in the ideal state is derived, thus demonstrating its periodic variation with time. In order to investigate the effects of air resistance and friction on the energy decay, the damping coefficient is further considered. The results reveal that under ideal conditions, the string’s energy fluctuates periodically, whereas with damping, it decays exponentially, thus affecting sound continuity and timbre stability.

With the increasing application of mathematics in modern society, a deep understanding of mathematical foundational theories becomes particularly important. This paper primarily investigates Pascal's Triangle and its three-dimensional extension, Pascal's Pyramid, and explores their properties and applications. The purpose of the study is to show their applications in different math-related areas, including algebra, probability theory, and combinatorial mathematics through literature review and mathematical modeling. This paper used case and data analysis to explore the relationships between Pascal's Triangle and the Fibonacci sequence, as well as Pascal's Pyramid and the Tribonacci sequence. The results show that Pascal's Triangle not only plays a role in binomial expansion, but also demonstrates its importance in trinomial expansions. This paper also preliminarily explores the generalization of Pascal's Triangle and Pyramid based on ab and abc models. By extending these models, this paper can offer new insights into their potential for advancing theoretical and applied mathematics, suggesting ways for future research in enhancing and applying these mathematical structures.

Accompanying the establishment of intimate economic and cultural connections between different countries and regions, people are required to travel through different places rapidly, which fosters the prosperity of the aviation industry and makes airplanes a crucial means of transportation. In 2024, however, plane crashes such as Azerbaijan Airlines Flight 8243 and Jeju Air Flight 2216 posed people’s concerns about the security of airplanes and the effectiveness of aviation systems. To that end, this study focuses on factors that influence plane crashes’ mortality and injury rate in order to find the most influential factor associated with plane crashes, aiming to be referenced to make rules protecting passengers’ safety during flights. At the same time, analyzing data on plane crashes can also avoid people’s unnecessary worries about plane crashes. This study uses random forest machine learning model to analyze plane crash data, which can effectively find the most important factor that will influence mortality and injury rates.

The utilization of bioelectrical signals, including Electromyography (EMG) and Electroencephalography (EEG), has substantially contributed to advancements in assistive technologies, medical diagnostics, and rehabilitation practices. However, research that combines these two technologies is still relatively scarce. This study focuses on exploring the integration of EMG and EEG signals for controlling robots, particularly for assisting elderly and disabled individuals in performing daily tasks. The experiment involved collecting hand muscle signals using surface EMG (sEMG) electrodes, an Arduino Uno, and an EMG shield. The participants were healthy adults, and the collected data was processed using Arduino and MATLAB software to analyze the signals and control the rotation of a servo motor. The results revealed a positive correlation between the intensity of the muscle signals and the motor’s rotational angle. Additionally, by integrating EEG and EMG, the system demonstrated improved accuracy in interpreting the participants ’ motion intentions, leading to a more precise control of the robotic movements. This research concludes that the combined use of EEG and EMG signals offers significant potential for improving control mechanisms in assistive robotics and neuroprosthetics, enabling more effective support for individuals with mobility challenges or disabilities. This approach also paves the way for more advanced applications in brain-computer interfaces (BCIs).

The brachistochrone problem is a classic optimization problem that aims to find the fastest descent path for an object from one point to another under the action of gravity, which has wide applications in physics, mathematics, and engineering. It has been studied through the variational method and the Euler-Lagrangian dynamic simulation problem, but there are still greater challenges in path optimization in complex media and real-time optimization in dynamic systems. And the paper explores the fundamental principles of the brachistochrone problem, emphasizing its physical background and the use of variational and parameterization methods to streamline the conventional solution. Besides, innovative approaches are presented to address particle motion in inhomogeneous media. The practical application of this problem in engineering is studied and discussed, including the metrology process in heterogeneous media, the progress of the signal numerical method combined with the optimization algorithm, and the potential in overcoming the limitations of the traditional analytical method is demonstrated. Thus, the results show that future research should pay more attention to solutions in complex physical environments and engineering applications, and boost the continuous development and application of related technologies.

With the development of information technology, mental health issues among information technology (IT) industry employees have become increasingly prominent and have become a focus of societal concern. However, there is a gap in current research on the mental health challenges faced by IT employees. This study addresses the inadequacies of existing literature on mental health impacts in IT workplaces, which are not comprehensive and have unclear results. Based on the Mental Health in Tech Survey dataset provided by Kaggle, this study employs quantitative research methods to conduct an in-depth analysis of the factors influencing the mental health of IT employees. The research results indicate that various factors in the work environment have a significant impact on employees' mental health. Based on the research findings, targeted improvement strategies and suggestions are proposed, emphasizing gender-sensitive health interventions and public education, to provide a reference for enterprises and policymakers, promote employee mental health, and enhance work efficiency, and drive widespread societal attention to mental health issues.