Highlights in Science, Engineering and Technology
Highlights in Science, Engineering and Technology is an open access, peer-reviewed publication series published by Darcy & Roy Press. It aims to publish conference proceedings dealing with all areas of science, engineering and technology.
Research on Measurement Methods for Silicon Carbide Epitaxial Layer Thickness Based on Optical Interference Principles
As a simple and non-destructive analytical technique, infrared interference spectroscopy is of great value in improving device manufacturing performance due to its ability to accurately measure epitaxial layer thickness. Based on a single-reflection and transmission model, this paper establishes theoretical models for calculating epitaxial layer thickness under two scenarios depending on whether the substrate refractive index is greater or smaller than that of the vacuum. By utilizing the property that substrates with higher carrier concentrations exhibit larger refractive indices, and combining the optical path differences between adjacent beams, an overall interference expression is derived from interference principles. This yields the relationship between fringe order and wavelength, leading to an algorithmic formula for epitaxial layer thickness. Meanwhile, variations in reflectivity are treated as shifts in interference peaks during experiments; adjacent peak values are extracted, corresponding wavenumbers and interference fringe orders are identified, and the thickness is calculated under a given angle of incidence. Under these conditions, two methods are employed to determine the refractive index of the epitaxial layer. In summary, this study provides a theoretical analysis of epitaxial layer thickness and verifies its accuracy through reliability assessments. The proposed methodological framework holds potential for broader application.
Silicon Carbide Epitaxial Layers, Dielectric Function, Infrared Spectroscopy, Refractive Index, Optical Interference.
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A Novel One-Dimensional Chaotic System and Its Application in Chaotic Communication Systems
Chaotic systems are widely applied in secure communications, and one-dimensional (1D) chaotic systems are preferred for resource-constrained scenarios due to their structural simplicity and ease of hardware implementation. However, traditional 1D systems (Logistic, Sine, Chebyshev maps) suffer from narrow/discontinuous chaotic intervals, insufficient sequence complexity, and weak initial sensitivity, leading to chaotic degradation in digital implementation and poor communication performance in practical channels. To address these issues, this paper proposes a novel 1D Sin-Coupled Nonlinear Map (1D-SCNM) based on “nonlinear fusion + parameter coupling”. It retains the low-complexity advantage of 1D systems while achieving wide continuous chaotic intervals, high-complexity sequences, and strong initial sensitivity. Evaluated via bifurcation diagrams, Lyapunov exponents (LE) and sample entropy (SE), 1D-SCNM was applied as a carrier in DCSK/NR-DCSK systems, with BER tested under AWGN and Rayleigh fading channels. Results show 1D-SCNM’s chaotic interval covers full parameters (LE/SE exceeding traditional systems); NR-DCSK (P=16) achieves a BER of 2.3×10⁻³ (14 dB Eb/N₀, AWGN), 97.2% improvement over DCSK (15.46 dB gain), with stable advantages in Rayleigh channels. This work provides a high-performance, easily implementable chaotic carrier for secure communications.
1D-SCNM, Chaotic Communication, Nonlinear Fusion.
A Survey of Statistical Models and Algorithms in Personalized Recommender Systems: The Case of Skincare Recommendation
In the era of information overload, personalized recommender systems are essential, particularly in critical domains such as skincare where incorrect suggestions have large physical risks. This presents a specialized problem whose demands for accuracy, explainability, and safety in the algorithms are unprecedented. This paper presents an extensive technical roadmap to the researcher, systematically examining the developmental history of recommender algorithms, covering the principal collaborative filtering and content-based filtering algorithms, the latent factor revolution with matrix factorization algorithms, and finishing with the newest deep learning and graph neural network-based algorithms for these systems. Some of this work covers the newest areas of research into how present systems can be trained to become "trustworthy decision partners", discussing causal inference for debiasing techniques, explainability techniques for building trust in users, and multi-dimensional, performance measures beyond accuracy. Using skin-care as a core subject, this paper examines how far the above paradigms are applicable to a very complex and critical real-world scenario. This will also provide an interesting view of future developments in hyper-personalized recommendation.
Personalized Recommendation, Skincare Recommendation, Matrix Factorization, Deep Learning, Graph Neural Networks.
A Study on the Factor Structure of Digital Skills of Manufacturing Employees in Foshan—Based on Exploratory Factor Analysis
In the context of digital transformation in the manufacturing sector, elucidating the internal structure of employees' digital skills is essential for talent development. Drawing on general ability theory, this study utilized 2025 survey data from industrial workers in Guangzhou, selecting a sample of 105 manufacturing workers from Foshan. An exploratory factor analysis was conducted to examine the underlying structure of six skills: equipment manual comprehension, equipment operation, programming problem solving, fault handling, data observation, and data analysis. Initially, the KMO test (0.772) and Bartlett’s test of sphericity (p<0.001) confirmed the suitability of the data for factor analysis. The findings revealed that all six skills could be attributed to a single underlying factor, termed “digital literacy,” which accounted for 69.1% of the total variance. Among these, “data observation” (loading 0.851) and “data analysis” (loading 0.846) emerged as the most critical dimensions constituting this core competency. This study substantiates the existence of a unified underlying structure for digital skills and provides empirical evidence for the development of a comprehensive training and assessment system centered on “digital literacy.” This study offers practical guidance for optimizing corporate human resource management and enhancing the efficiency of digital transformation.
Digital Literacy, Manufacturing Employees, Exploratory Factor Analysis, Skill Structure.
A High-Order Numerical Scheme for Allen-Cahn Equation via Strang Splitting and Fourier Spectral Method
This paper proposes a practical numerical scheme for solving the Allen-Cahn (AC) equation by integrating Strang operator splitting, the Fourier spectral method, and SSP-RK (strong stability-preserving Runge-Kutta) time integration. This approach enhances the stability of phase-field simulations while ensuring computational efficiency by decoupling the treatment of stiff nonlinear terms and linear diffusion terms: the nonlinear reaction term is explicitly advanced using SSP-RK, leveraging its strong stability-preserving properties to control solution boundedness under moderate time step sizes; the linear diffusion term is solved exactly via Fourier spectral differentiation, significantly reducing the iterative cost of traditional implicit schemes. Spatial discretization employs the spectral method, achieving superior interface resolution compared to finite differences in regular domains. Numerical verifications demonstrate that: under a moderate stiffness parameter ( ), when the time step size is refined to 0.00625, the error stably decreases from an initial to , with convergence properties approaching the theoretical second-order accuracy; under strong stiffness regimes ( ), the scheme maintains effective convergence trends, with error reduction magnitudes reaching an order of magnitude. Physical property verifications confirm that the scheme strictly preserves the maximum principle (phase-field values always lie within the [0,1] interval) under two/three-dimensional random initial conditions, and the discrete energy exhibits monotonic decay characteristics consistent with the evolutionary laws of the double-well free energy. Computational efficiency tests show that, for moderate-scale problems, the scheme saves approximately 30–40% of computational time compared to standard implicit schemes. This scheme provides a new option balancing accuracy and efficiency for phase-field modeling, though its strong stiffness adaptability and large-scale scalability still require in-depth study.
Allen-Cahn Equation, Strang Splitting Method, Fourier Spectral Method, SSP-RK, Error Analysis.
Study on the Transmission Effect of Interest Rate Decline on Housing Price in Structural Deflation Cycle (2023-2025)
During economic downturns, particularly deflationary periods, the transmission of interest rates to real estate prices poses a complex and challenging issue for central banks worldwide. The intertwining of various economic issues and black swan events continuously hinders this transmission mechanism, repeatedly weakening the effectiveness of interest rate policies and making it difficult for single-rate measures to effectively break the downward spiral in housing prices. This paper focuses on the specific context of China's economic downturn since 2019, examining the transmission effect of interest rate policies on real estate prices through regression analysis. It explores how interest rate policies interact with property values while simultaneously influencing investment and consumption patterns. The research finds that during structural deflation, interest rate cuts have a short-term positive impact on housing prices, with current and one-period lagged rates showing significant effects. However, the transmission mechanism is severely weakened in the long run. This inefficiency is attributed to three key bottlenecks: high household debt saturation, liquidity traps for developers, and self-reinforcing deflationary expectations. The research concludes that traditional monetary policy is systemically ineffective in this environment, necessitating more targeted, integrated policy measures. It extends the financial accelerator model and provides empirical support for targeted monetary policies.
structural deflation, interest rate policy, transmission effect.
Research on the Application of Deep Learning Models in Time Series Data
In today's digital age, In the digital age, the importance of time-series data is increasingly evident across finance, industry, IoT, and healthcare, with its volume growing rapidly. According to IDC projections, global data volume will reach 175 ZB by 2025, with approximately 79.4 ZB originating from IoT devices—much of it existing in time-series formats. However, efficiently and accurately extracting underlying patterns from massive, high-dimensional datasets to enable reliable predictions remains a core challenge for both academia and industry. Traditional time series models (e.g., ARIMA) struggle to capture complex nonlinear patterns, while deep learning models (e.g., LSTM, Transformer) face performance limitations due to hyperparameter selection and training strategies. Existing tuning processes lack automation and are prone to overfitting.This study proposes a systematic framework integrating automated hyperparameter optimization with deep learning training to enhance the accuracy, efficiency, and generalization capabilities of time series forecasting. Using data from Australia's electricity market (2006–2011), This article compared several models for load forecasting, including linear regression, Lasso, ARIMA, random forests, TCN, and an enhanced Transformer. This article used K-fold cross-validation, grid and Bayesian optimization, early stopping, and adaptive learning rate decay. The enhanced Transformer achieved the best performance (MAE ~70 MW, RMSE ~90 MW, R² ~0.995), outperforming other models. ARIMA underperformed due to its lack of exogenous variables. The Transformer showed robustness across seasons. Future work could combine TCN's local feature extraction with the Transformer's global dependency modeling.The time series forecasting framework proposed in this study effectively enhances prediction accuracy and model generalization capabilities. Transformer models demonstrate superior performance in forecasting complex dynamic changes. Future research may integrate the strengths of different models to expand their applications across multiple domains.
Time Series Forecasting, Transformer Model, Hyperparameter Optimization.
Elementary Mathematical Inequalities to Prove the Laws of Large Numbers
This paper gives a simple and clear proof of the Weak Law of Large Numbers (WLLN) and the Strong Law of Large Numbers (SLLN). We only use basic tools from real analysis and elementary probability. First, we prove Markov’s inequality, Cheby- shev’s inequality, and the Borel–Cantelli lemma in a direct way. We also give a proof of Kolmogorov’s maximal inequality. After that, we use these inequalities to prove the WLLN with Chebyshev’s inequality and the SLLN with Kolmogorov’s inequality and the Borel–Cantelli lemma. The main goal of this paper is to show that the laws of large num- bers can be proved with simple ideas, without advanced probability theory. Our work helps beginners understand these important results in a more easy and friendly way.
Statistics, Applied mathematics, Chebyshev’s inequality, Markov’s inequality, Borel–Cantelli lemma, Kolmogorov’s maximal inequality, WLLN, SLLN, LLN.
Research on Dynamic Modeling of Multibody Systems Based on Equiangular Helix Motion
Focusing on the motion characteristics of multi-body equidistant spiral motion, this paper takes the "bench dragon", a traditional folk activity in the Zhejiang-Fujian region, as an example to establish a dynamic mathematical model based on the equidistant spiral trajectory. It realizes numerical solution and analysis through MATLAB, and explores the motion trajectory of complex multi-body joint motion systems in equidistant spiral motion.In this paper, the differential equation of the spiral is derived through geometric relations, and the evolution laws of position and velocity during the initial coiling process of the spiral are studied. Combined with the rigid body fixed-axis rotation model and the constant velocity condition at the starting point of equidistant spiral motion, the fourth-order Runge-Kutta method and nonlinear equations are used to solve, so as to accurately calculate the position and velocity data of each physical motion in multi-body equidistant spiral motion. At the same time, focusing on the collision of each equidistant spiral motion, the overlap is determined by coordinate discretization and rotation matrix method, which further reveals the collision constraint mechanism of the multi-body joint motion system in the close cooperative motion.This paper not only provides a scientific basis for optimizing the motion trajectory of traditional folk activities, but also offers important theoretical references and methodological inspirations for fields such as motion planning, collision avoidance and cooperative control of complex joint multi-body systems, and has broad application prospects.
Equidistant helix, Fourth-order Runge-Kutta method, System of nonlinear equations, Dynamic modeling of multibody systems
Non-destructive measurement of SiC Epitaxial Layer Thickness Using FTIR Spectroscopy with Cauchy Dispersion Optimization
Accurate measurement of SiC epitaxial layer thickness is crucial for third-generation semiconductor device performance. This paper proposes a comprehensive measurement method combining interference optics principles with Cauchy dispersion model and numerical optimization algorithms. The method establishes a thickness solution model based on interference fringe extrema identification in FTIR reflection spectra. A nonlinear least-squares optimization algorithm jointly optimizes thickness and dispersion coefficients. To address multi-beam interference and phonon resonance effects near 797 cm⁻¹, we develop compensation strategies including K-M transformation and frequency-domain filtering. Experimental validation using FTIR spectra at 10° and 15° incident angles demonstrates excellent measurement accuracy: the epitaxial layer thickness is determined as 8.06 ± 0.41 μm, with relative deviation less than 0.15% between different angles. The theoretical model shows strong agreement with experimental data (correlation coefficient 0.89 in non-resonant regions). This method provides reliable technical support for quality control in SiC manufacturing, meeting industrial requirements with measurement uncertainty below 5%.
Epitaxial Layer Thickness, Interference Optics, Cauchy Dispersion, FTIR Spectroscopy, Non-Destructive Measurement.
Medal Prediction for the 2028 Los Angeles Olympic Games Based on Lasso Regression and Logistic Regression Models
The Olympic Games are among the most-watched sporting events globally, offering a platform to showcase top-tier athleticism and highlighting the progress of nations in the sports sector. As countries aim to enhance their global image, Olympic achievements hold significant value beyond sports, influencing international reputation and recognition. This report focuses on developing a predictive model to forecast the medal standings for the 2028 Los Angeles Olympics. This paper proposes a comprehensive approach integrating various factors such as historical performance and athlete data. By leveraging models like Lasso regression and logistic regression, this paper analyzes data on medal distribution and the potential impact of coaching expertise. The results highlight the predicted medal rankings, offering insights into emerging trends and countries likely to perform exceptionally well. This predictive modeling framework is not only valuable for future Olympic predictions but also enhances our understanding of the complex factors driving Olympic success, contributing to a better grasp of sports industry dynamics and international positioning.
Olympic medals, Lasso Regression, Logistic Regression.
Predicting The Medal Distribution of Countries in the 2028 Los Angeles Olympics Based On OP-Xgboost
This study aims to predict the medal distribution of various countries at the 2028 Los Angeles Olympics. Through data cleaning and feature engineering, a dataset was constructed that includes key indicators such as population size, GDP, per capita income, and sports development index.Innovatively proposed and applied the XGBoost model combined with the Optuna hyperparameter optimization framework (OP-XGBoost), significantly improving the model's prediction accuracy (medal count prediction R² increased from 0.636 to 0.716, and gold medal count R² increased from 0.563 to 0.635). The model prediction results show that the United States will maintain its dominance in sports, it is expected to win a total of 138 medals (46 gold medals), with a prediction range of [88, 140]; China closely follows, expected to win 97 medals (42 gold medals), with a prediction range of [24, 52]. Countries like the UK and Japan are expected to be in the second tier. An analysis of national performance trends indicates the United States has made the most significant progress (+92.5%), mainly due to the continuous increase in sports investment; on the other hand, the Unified Team's performance is expected to decline significantly (-77.9%), possibly due to the instability in the development of its athlete pipeline. This study provides a quantitative analysis to understand the relationship between a country's overall strength and its Olympic performance, verifies the effectiveness of machine learning in sports prediction, and offers data support and model references for countries to develop differentiated Olympic preparation strategies.
Optuna, XGBoost, Medal Prediction Model.
Predicting Olympic Medal Counts by Bootstrap-Enhanced Gradient Boosting Machine with Log-Transformed K-Means Clustering
Olympic medal counts serve as a critical indicator of a nation's comprehensive sports strength. Accurate predictions offer distinctive perspectives for strategic resource allocation. To handle the strongly skewed distribution featuring long tails in medal data and capture complex nonlinear relationships among variables, this study proposes a hybrid methodology combining log-transformed K-means clustering and Bootstrap-Enhanced Gradient Boosting Machine (BEGBM). Countries are stratified into five strength tiers (e.g., elite to bottom) via K-means clustering on log-transformed medal features, reducing skewness bias. A robust BEGBM model trained on bootstrap samples (B=150) incorporates fluid sports variables and clustered tiers, with missing values imputed by random forests. The work presented here is the first to integrate tiered and mindful of uncertainty GBM into medal prediction. The model achieves RMSE=1.16 (gold)/1.91 (total), MAE=0.33/0.81, and <!-- [if gte msEquation 12]><m:oMath><m:sSup><m:sSupPr><m:ctrlPr></m:ctrlPr></m:sSupPr><m:e><m:r>R</m:r></m:e><m:sup><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>2</m:r></m:sup></m:sSup></m:oMath><![endif]--> <span lang="EN-US" style="font-size: 10.5pt; mso-bidi-font-size: 11.0pt; font-family: 等线; mso-ascii-theme-font: minor-latin; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; position: relative; top: 2.5pt; mso-text-raise: -2.5pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;"> =0.50/0.61. It further provides 95% CIs for the 2028 Los Angeles Olympics (e.g., USA: [35.8, 42.7] gold medals) and identifies nations with significantly changing medal potential. This data-based method offers sports authorities with a dependable tool for optimizing resource investment.
Gradient Boosting Machine, Bootstrap Sampling Algorithm, Log-transformed k-means Clustering, Prediction Model.
Product Production Decision Model Based on Cost Minimization
To achieve maximum profit, controlling costs during the production process has become a top priority in enterprise production planning. A certain enterprise needs to manufacture and sell a finished product by purchasing different spare parts and assembling them in order to produce an electronic product. This article establishes a product production decision model based on cost minimization, which helps enterprises make the most reasonable production decisions and achieve maximum profits. This article establishes a decision-making model for the sampling and testing plan of spare parts based on hypothesis testing method. According to the central limit theorem in statistics, the original distribution is followed when the sample size is small, while the normal approximation can be used instead of the original distribution when the sample size is large. The calculation result is as follows: In (1), if the sample size n=29, the enterprise should reject this batch of spare parts when the number of defective products reaches 6; If the sample size n=1000, the enterprise should reject this batch of spare parts when the number of defective products reaches 116. In (2), if the sample size n=29, the enterprise should reject this batch of spare parts when the number of defective products reaches 5; If the sample size n=1000, the enterprise should reject this batch of spare parts when the number of defective products reaches 113.This article transforms the problem of maximizing final net profit into the problem of minimizing final cost value, and establishes a product production decision model based on the minimum cost value. This article mathematizes the five decision points that exist in the production process and sets corresponding variable decision variables n=1,2,..., 5, xn values of 1 or 0 to express whether the decision is to be executed or not. After obtaining all decision options through enumeration, calculate the cost value corresponding to each option, and take the decision option corresponding to the lowest cost value as the best decision option in this situation.
Statistics, Hypothesis testing, Central limit theorem, Normal approximation, Z-test.
Determination of Silicon Carbide Epitaxial Layer Thickness Based on Genetic Algorithm and Transfer Matrix Model
This paper focuses on determining the thickness of silicon carbide epitaxial layers using infrared interferometry. A mathematical model was established based on the principle of double-beam interference, incorporating Snell’s Law and the Pythagorean theorem to calculate the optical path difference between two reflected beams (from the epitaxial layer surface and the substrate interface). The phase difference was linked to the interference order, and conditions for constructive and destructive interference were analyzed to derive the fundamental thickness model. The Sellmeier dispersion model was introduced to account for the wavelength-dependent refractive index influenced by doping concentration. For experimental verification, the reflectance spectra were preprocessed to remove noise and convert wavenumbers into wavelengths. Extreme interference points were identified, and thickness was optimized globally using genetic algorithms in MATLAB, minimizing the least-squares error between modeled and measured reflectance. Reliability was confirmed through residual analysis and consistency across incidence angles. The impact of multi-beam interference was analyzed by comparing its characteristics with double-beam interference and identifying necessary conditions (e.g., high reflectivity and phase stability). The coefficient of variation in wavenumber spacing was used to multi-beam effects. For silicon wafers, the transfer matrix model and genetic algorithms were employed to calculate optimized thickness, accounting for multi-beam interference. This work provides a robust framework for high-accuracy, nondestructive thickness measurement of epitaxial layers.
Genetic Algorithm, Transfer Matrix Model (Tmm), Sellmeier Equation, Spectral Data Inversion.
Study on the Influencing Factors and Correlation of Fetal Y Chromosome Concentration in NIPT Based on Ordered Clustering and Linear Regression
To address the issue of individual differences affecting the accuracy of non-invasive prenatal testing (NIPT), especially the pain point of low free DNA concentration in the fetus of pregnant women with high BMI, this study analyzed the correlation between the concentration of the Y chromosome in the fetus and the gestational age and BMI of pregnant women. First, samples with abnormal GC content (not 40% to 60%) were excluded through data preprocessing. Then, histograms and scatter plots were drawn to initially observe the distribution and correlation characteristics of the variables. It was found that the scatter plot was difficult to visually determine the correlation. Subsequently, a grouped regression strategy was adopted: BMI was grouped by equal frequency, gestational weeks were determined based on the Jenks natural breakpoint method, combined with variance goodness-of-fit (GVF), pseudo-F statistics, Bayesian information criterion (BIC), and entropy weight method - TOPSIS method to determine the optimal 15 groups. After taking the mean of each group of variables, a univariate linear regression model was constructed, and the significance was verified through the F-test. The results showed that the concentration of the Y chromosome was significantly positively correlated with the gestational weeks (r= 0.6338, P=0.0112), and the degree of correlation was moderate. It was extremely significantly negatively correlated with BMI (r= -0.8658, P=0.0054), and the degree of correlation was relatively strong. This study provides data support for optimizing the timing of NIPT detection and improving the accuracy of detection in pregnant women with high BMI.
Non-invasive prenatal testing (NIPT), Y chromosome concentration, Jenks natural breakpoint method, linear regression, significance test.
LGBM-Based Real-Time Analysis of Tennis Player Performance
This study aims to develop a real-time performance evaluation model for tennis players, enabling the quantification of match dynamics and the identification of key factors influencing scoring outcomes. Utilizing data from the Wimbledon Open dataset, the research applies preprocessing techniques such as outlier removal to construct a two-level indicator system encompassing psychological, physiological, and service-related variables. A binary logistic regression analysis is conducted to test indicator significance, followed by a comparative evaluation of five machine learning algorithms: LGBM, XGB, SVC, MLP, and LR. Results demonstrate that the LGBM algorithm outperforms others, achieving an accuracy of 0.69 and an AUC of 0.77. The model effectively captures real-time player performance and provides actionable data support for tennis training and tactical decision-making. Future improvements may focus on refining the indicator system to enhance the model’s generalizability and predictive robustness.
Tennis Players, Real-Time Performance, LGBM Algorithm, Machine Learning, Indicator system.
Prediction Of Tennis Players' Court Behaviors Based on The Xgboost Model and The Shap Model
In tennis competitions, coaches and athletes are in urgent need of quantifiable indicators to comprehensively assess the game situation and make timely tactical adjustments. To meet this crucial demand, this article constructed a "momentum" evaluation and prediction model. Initially, this article conducted an in - depth analysis to screen out variables that impact a player's on - court performance, systematically dividing them into two major categories: game - wide variables and local variables. This article placed particular emphasis on local variables, as they capture the essence of a player's outstanding plays, such as powerful aces or incredible retrievals, which can significantly shift the momentum of the game. This influence is effectively represented through a sophisticated weighting mechanism.Based on the robust XGBoost model, this article’s prediction model is not only highly efficient in processing and analyzing data but also highly practical for real - time application during matches. By quantifying the momentum of both players, it provides valuable support for immediate strategy adjustments. Moreover, the model can generate detailed reports and suggestions based on the momentum data, offering targeted guidance for athletes' daily training and helping coaches formulate more scientific training plans, thus enhancing the overall competitiveness of the players.
Momentum Quantitative Scoring Model, XGBoost Regression Model, Shap Model.
A Study on Hyperparameter Tuning of Twin Support Vector Regression Based on Bayesian Optimization
This study addresses the challenge of optimizing the predictive performance of Twin Support Vector Regression (TSVR) models on complex datasets by employing Bayesian Optimization (BO) for automatic hyperparameter tuning. As an enhanced variant of Support Vector Regression (SVR), TSVR achieves significantly greater computational efficiency by solving two smaller-scale quadratic programming problems. Within the Bayesian optimization framework, the construction of a posterior probability model enables efficient exploration of the hyperparameter space, thereby overcoming the inefficiency limitations of traditional methods. Experimental validation demonstrates that the BO-optimized TSVR model achieves significant reductions in Mean Squared Error (MSE) across multiple synthetic datasets, while simultaneously exhibiting superior predictive accuracy and generalization capability. The significance of this research lies not only in its improvement of TSVR model performance but also in its provision of a novel approach for hyperparameter optimization in machine learning, possessing substantial theoretical and practical merit.
Twin Support Vector Regression, Bayesian Optimization, Hyperparameter Tuning, Regression.
Analysis Of Staircase Wear Degree Based on Monte Carlo Simulation
Based on Archard’s friction theory, an Archard model considering both anthropogenic wear (related to gait, material hardness, and wear coefficient) and environmental weathering wear is established to predict stair wear depth distribution. A probabilistic model for pedestrian footprint distribution is developed using the beta function (for footfall timing), two-dimensional normal distribution (for footfall center), and random step angle deflection. Monte Carlo simulation is applied to generate random pedestrian stepping events, simulating movement tendencies (up/down) and habits (single/side-by-side walking). Model validation shows good agreement between predicted wear volume (15540 cm³) and actual data (15303 cm³). Sensitivity analyses confirm model stability. Results indicate that step wear morphology can infer pedestrian habits, step age, and refurbishment history, providing valuable references for ancient site research.
Archard Equation, Monte Carlo simulation, Wear depth, Normal distribution.
Research On Multi-Stage Production Inspection and Decision Optimization Based on Dynamic Programming
This paper addresses the quality control and cost optimization issues in the multi-stage production of electronic products by constructing a multi-stage production strategy model and dynamic adjustment mechanism based on dynamic programming. By quantifying the cumulative effect of defective rates, it was calculated that the cumulative defective rate for semi-finished products reaches a maximum of 0.271, while that for finished products reaches 0.569. An optimal path was designed: "Inspect seven parts, not inspect all semi-finished products, and not inspect but disassemble finished products." This reduced total cost to 88.2392 yuan, with only 5.6% of the loss due to defective products. The dynamic adjustment mechanism employs Wilson interval improvement estimation, which reduces the error by 23.8% with a sample size of 10 and avoids losses of 32 yuan in the scenario of a sudden change in defective rate. Simulation data shows that compared with the traditional strategy, the total cost is reduced by 14%, the qualified finished product rate increases by 5.2 percentage points, and the proportion of inspection costs decreases by 7.5%, verifying the model's effectiveness in balancing quality and cost.
Dynamic Programming; Defect Rate Accumulation; Decision Optimization; Wilson Interval; Multi-Stage Production.
Deep Learning Fusion Model Based Electricity Load Forecasting for Extreme Weather
Aiming at the problem of insufficient accuracy of power load forecasting in extreme weather, a spatio-temporally aligned database is constructed based on the multi-source data (including 15-minute-level load profiles, 0.25°×0.25° gridded meteorological data, and EM-DAT standard disaster records) for the provincial power grids in the years 2015-2023. Fifteen key indicators are screened out by the random forest algorithm, and the hybrid LSTM-XGBoost model is innovatively proposed and dynamically weighted and optimised by Lasso regression. Tests show that the RMSE of the model is controlled in the range of 2.49~3.16 under typhoon weather, and the accuracy is improved by more than 45% compared with a single model. In the extreme high temperature event in North China in 2023, the prediction error of the model 6 hours in advance is only 4.7%. The technique has been validated in actual grid operation, providing reliable decision support for extreme weather power dispatch with important engineering application value.
Deep learning; Extreme weather; Power load forecasting; Long and short-term memory network; XGBoost.
Sustainable Development Research of Organic Agricultural Ecosystem Based on System Dynamics Model
The conversion of forests to agricultural ecosystems has become an increasingly prominent trend worldwide. Against this backdrop, this article employs system dynamics modeling to delve into the sustainable development pathways of organic agricultural ecosystems, aiming to provide valuable insights for practice and research in related fields. In order to explore the ecological stability of forests converted to agricultural land, based on ecological causality and food web theory, this article constructs a species dynamics model for the corn food chain, analyzes the changes in species numbers before and after the use of pesticides and herbicides, and finds that chemical agents benefit agriculture in the short term, but destroy the ecological balance in the long term. In order to study the impact of species recolonization, this article elucidated relevant indicators and models, analyzed the trend of indicators after the introduction of soybeans and stinkbugs, and came to the conclusion that soybeans help to improve the stability and stinkbugs destabilize the ecological balance in the short term. Exploring the impacts of human decision-making, it was found that discontinuing the use of herbicides improved stability and biodiversity, and that the introduction of bats was more effective than that of gray starlings. The innovation of this study lies in constructing system dynamics models and differential equations to comprehensively analyze the impacts of multiple factors, accurately distinguish the roles of different species in different stages, propose and evaluate specific organic agricultural strategies, thereby providing a scientific basis for the sustainable development of agricultural ecosystems.
Agricultural ecosystem, Chemical agents, Species recolonization, Ecological stability, System dynamics modeling.
Green Vehicle Routing Optimization in Urban Traffic Congestion Environment Based On K-Means Clustering and Genetic Algorithm
As urban traffic congestion becomes increasingly severe, supply chain transportation faces the dual challenges of declining efficiency and mounting environmental burdens. To address this, this study constructs a Green Vehicle Routing Problem (GVRP) framework that integrates real-time traffic information. First, K-means clustering technology is employed to classify urban road networks by congestion levels, establishing a three-tier classification system of low, medium, and high congestion zones. Subsequently, polynomial regression methods are utilized to establish a quantitative relationship model between vehicle speed and carbon emission intensity. Based on this theoretical foundation, a multi-objective optimization framework is designed that comprehensively considers environmental costs and traffic impedance factors, with performance comparison tests conducted between genetic algorithms and classical shortest path algorithms. Experimental results demonstrate that genetic algorithms perform excellently when handling high-congestion road segments, significantly reducing carbon footprint while shortening transportation cycles. This research provides scientific basis and operational paradigms for enterprises to construct sustainable supply chain networks based on dynamic traffic information.
Vehicle Routing Optimization, Genetic Algorithm, Shortest Path Algorithm, K-means Clustering Analysis.
Research On Optimal Planting Strategy of Crops Based on Nonlinear Programming and Monte Carlo Optimization Simulation
This article addresses the issue of crop planting conditions and optimal planting plans, using a nonlinear programming method based on Monte Carlo optimization, visualization processing, sensitivity analysis, and Pearson correlation coefficient analysis. The relationship between the optimal planting plan and various influencing factors such as planting land, crop name, crop type, planting area, and sales unit price is obtained, as well as how to determine the optimal planting plan (i.e. maximum revenue). It is required to find the optimal planting plan for two different sales situations within the limited area of four plots and two greenhouses, as well as various restrictions such as the inability to plant continuously on the same plot and the need to plant different types of crops on different plots. Firstly, preprocess the data to calculate the sales unit price based on the median, and in order to make reasonable use of land resources, multiple types of land can be used on one site; Secondly, using nonlinear programming methods, the restrictive conditions are processed and transformed into mathematical equations, and the rules are summarized and visualized through a lingo processor for analysis; Finally, using the objective function and the optimal planting plan provided by the lingo processor, the maximum profit under two different sales scenarios is obtained, which is denoted as yuan.
Nonlinear programming model, Monte Carlo optimization, Sensitivity analysis, Planting strategy planning, Maximum revenue.
A Study on Olympic Medal Prediction Based on Random Forest and Polynomial Regression
The Olympic medal table serves as a symbol of a nation's sporting competitiveness, and fluctuations in medal counts reflect underlying patterns within complex data. This study aims to uncover the mathematical logic behind the competition for medals and to identify the intrinsic relationships between these patterns and historical data. Based on attributes that reflect a country's medal-winning potential, a predictive model is constructed to estimate medal counts with a high degree of accuracy. Specifically, six key factors influencing medal counts are identified and integrated into a random forest regression model. A clustering model based on comprehensive indicators is applied to classify and quantify countries according to their Olympic performance. Polynomial regression is then employed to forecast relevant data for the 2028 Olympic Games. These forecasts are subsequently used to predict the number of medals in 2028 using the trained random forest model, and prediction intervals are established based on the MAPE error range.The model’s performance is evaluated using MSE, MAE, and R2 metrics for gold, silver, bronze, and total medal predictions. Results show low prediction errors and strong goodness-of-fit, with R² values of 0.93588, 0.96743, 0.96554, and 0.83254, respectively. These outcomes indicate that the model demonstrates high predictive accuracy and robustness across all medal categories.
Medal Prediction, Clustering Model, Random Forest, Polynomial Regression.
Partial Linear Additive Integrated Regression Models Based on Functional Gaussian Processes
In this paper, proposing a partially linear additive Gaussian process-based integration model for regression problems containing functional-type and vector-valued predictor variables. The model downscales high-dimensional functional data by functional principal component analysis, extracts low-dimensional principal component scores, and constructs additive Gaussian process sub-models, i.e., the non-linear relationship between functional predictor variables and response variables is fitted by independent Gaussian process components, and the vector-valued predictor variables are selected by the linear portion of Lasso regularisation for variable selection. To enhance the model generalisation ability, the predictions of each sub-model are adaptively fused using the Stacking integration strategy. Simulation experiments show that the proposed method can effectively identify irrelevant vector-type variables and significantly outperforms the traditional functional linear model in terms of prediction error; real data analysis further validates its competitiveness in prediction tasks. In addition, the framework proposed in this paper is highly scalable: the feature representation of functional variables can be optimized by introducing multi-kernel learning, and the computational complexity can be reduced by combining with sparse Gaussian process, which can be extended to dynamic data flow modelling or combined with deep integration methods in the future, to provide a flexible and interpretable modelling paradigm for complex and heterogeneous data.
gaussian process regression; partial linear models; functional principal component analysis; Stacking integration.
Optimization and Risk Assessment Application of Financial Time Series Forecasting Models Based on Machine Learning
Financial time series forecast has always been a difficult question because capital market is inherently nonlinear and noisy. Traditional econometric models can't catch the complicated patterns so people have lots of interest in machine learning (ML), deep learning. This paper studies how to optimize and apply advanced neural networks such as LSTMs and GRUs in financial prediction tasks. We propose a framework for hyperparameter optimization with Bayesian optimization, and show that this approach outperforms random parameter selection. We take daily closing prices from the SP500 index over a ten-year period and compare the results of optimized models against both traditional statistics based benchmarks (ARIMA) as well as non-optimized ML models. The Results show that hyperparameter training gives considerable improvement in forecasting accuracy as optimized GRU shows Lowest RMSE and MAE. And also, the better forecasts from this study are proven practical with the aid of a risk assessment framework. We use the prediction outputsto find out the Value -at -Risk, or VaR, and this shows that the better forecasts that we get from the model that has been adjusted are able to give us more exact and correct information about risks. This kind of information is very important when it comes to taking care of our money, and following what the bosses say. This research points out how important it is to properly fine-tune models when we use ML stuff for finance stuff and shows us that such improved models really can make our work with numbers better.
Financial Time Series, Machine Learning, LSTM, GRU, Model Optimization, Hyperparameter Tuning, Risk Assessment, Value-at-Risk (VaR), Bayesian Optimization.
Correlation Analysis between Regional Online Environmental Information Attention and Local Scale Green Finance
In today's world, with the advancement of technology, the living standard of mankind has ushered in a huge leap. However, problems such as environmental pollution are also increasingly apparent, which has attracted great attention from China and other countries. In this context, the research on green finance is particularly important. Combining with the situation that the public expresses their views widely through the Internet in the network era, this paper further explores the correlation between the attention of environmental-related information in the regional network and the local scale of green finance, and establishes the relevant specific model. This paper mainly studies the correlation between the attention of environmental-related information in the regional network and the scale of local scale of green finance through the Spearman correlation coefficient, and explores the trend of the correlation over time. This paper found that there is a significant positive correlation between the two, and this correlation has an increasing trend year by year. Finally, this paper uses a linear regression model and a BP neural network to complete the related modeling. This study shows that the formulation of green finance related policies can reasonably guide people to join in the construction of green finance. Furthermore, the model of this study can also be used to quantitatively predict the impact of residents' participation on the development of green finance to a certain extent, so as to promote the progress of green finance.
green finance, public attention, Spearman correlation coefficient, linear regression model, BP neural network.
A conjecture about the orthogonal vector equations associated with the Hadamard matrix
The investigation of Hadamard matrices provides an ancient problem in algebra which has extensive links to various real-world applications, such as signal transformation. In this work, we investigate a conjecture on the form of the solution corresponding to a special case of 6×6 complex Hadamard matrices. Establishing this conjecture will substantially influence the development of so-called non-H2-reducible Hadamard matrices. To build our case, we first establish two encompassing lemmas based on the geometric properties of unit modulus complex numbers with sum zero. Then, using these lemmas we establish the conjecture for various special cases. Finally, we take the general form of the problem and simply it down to a system of trigonometric equations. The numerical evidence presented give strong evidence of validity suggested a potential path for a complete proof.
complex number; orthogonal vector; plane and analytic geometry.