Mathematical Modeling and Algorithm Application
Mathematical Modeling and Algorithm Application (MMAA) is a peer-reviewed journal published by Darcy & Roy Press. The mission of the journal is to provide an academic forum for discussing the issues of mathematical modeling, algorithm application, theoretical and applied mathematics across the world. All articles published are rigorously and fast reviewed meeting the Journal Quality standards.
Dynamic Hyper-Parameter Adjustment in Fedprox for Performance Optimization in Federated Learning
This paper investigates the application of dynamic hyper-parameter adjustment strategies to improve the performance of the FedProx algorithm in federated learning (FL). FedProx addresses the challenges posed by data heterogeneity across clients, a common issue in FL that hinders convergence. While FedProx improves upon the basic FedAvg algorithm by introducing a proximal term to stabilize model updates, the hyper-parameter μ that controls the impact of the proximal term is sensitive and needs careful tuning. An inappropriate μ can degrade performance, making dynamic adjustment crucial. The study introduces two dynamic μ adjustment strategies. The first strategy, called ExponentialDecay, progressively reduces μ exponentially by multiplying it with a constant factor. The second strategy, AdaptiveLoss, adjusts μ based on changes in the loss value, decreasing it when the loss decreases and increasing it when the loss increases, offering a more responsive approach to the model’s performance. The effectiveness of both strategies is evaluated on the EMNIST dataset, which simulates real-world non-IID data distributions. Results show that both dynamic strategies outperform the static μ setting in terms of model accuracy, loss reduction, and training speed, particularly in scenarios with highly heterogeneous data. Specifically, the AdaptiveLoss strategy achieves the best performance when the data is extremely non-IID, reducing loss by 10.2% and improving accuracy by 2.5% compared to the static μ approach. These dynamic strategies not only enhance FedProx’s stability but also accelerate the convergence of the global model.
Copyright (c) 2026 https://creativecommons.org/licenses/by-nc/4.0
Research and Analysis on the Mechanism of Suppressing Large Model Hallucination Based on Modular RAG Architecture
Large Language Models (LLMs) perform remarkably well in knowledge-intensive tasks, yet they are difficult to deploy in high-stakes scenarios due to 'hallucinations'—outputs that contradict factual information. Although Retrieval-Augmented Generation (RAG) is widely regarded as a mainstream approach to mitigate hallucinations, most existing studies treat it as a black box and rarely analyze the heterogeneous functions of its internal modules. To address this, we propose a 'functionally decomposed' modular RAG taxonomy, dividing the entire process into three stages: retrieval, refinement, and generation, from which three technical pathways are derived: Direct Injection RAG (DI-RAG), Relevance-Focused RAG (RF-RAG), and Fact-Checking RAG (FC-RAG). Utilizing the large-scale real-world Q&A dataset MS MARCO, we constructed four benchmarks simulating high-risk scenarios such as information noise, knowledge conflicts, and outdated knowledge. Using Qwen1.5-7B-Chat as the generative backbone, we systematically evaluate the marginal benefits of the three architectures in suppressing hallucinations and quantify the contributions of components like re-rankers and multi-query verifiers in specific hallucination scenarios, providing actionable empirical guidance and optimization pathways for building high-fidelity RAG systems.
Collaborative Model of Business Analysis and Data Analysis in the Era of Big Data-Taking Retail Industry as an Example
The retail industry is closely related to people's lives and is also a driving force for the development of the national economy. This article focuses on studying the dynamic changes of the retail industry in the commercial market under the premise of rapid economic and social productivity development. In the past, people usually used past experience to predict the future market, but there was no definite support, and there would often be large errors, as well as face some unavoidable crises. However, in the current era of data informatization, relatively accurate predictions of the future market can be made through a large amount of data, while avoiding losses caused by some crises. This study employed various analytical methods to analyze the past and current situation of the retail market. This article further reveals the three major problems existing in traditional retail analysis: the separation of data analysis and business needs; the lack of data support for experience-based decision-making; and severe departmental data barriers. Finally, implementation suggestions are proposed from three aspects: data governance, talent cultivation, and organizational optimization, providing a systematic solution for the retail industry to enhance its decision-making ability and market competitiveness.
Adaptive Confidence-Driven Sample Selection with Alignment Loss for Efficient Federated Active Learning
Federated Active Learning (FAL) aims to reduce labeling costs by selecting the most informative samples for annotation while preserving strong model performance. However, current FAL methods struggle with the challenge of client heterogeneity in non-IID environments, often leading to suboptimal sample selection and increased computational burden due to repeated inference on unlabeled data. To address these issues, we propose a novel approach called Adaptive Confidence-Driven Sample Selection (ACdSS), which combines the CHASe strategy with Alignment Loss to improve sample selection efficiency. ACdSS leverages dynamic confidence scores to assess uncertainty in unlabeled data and identifies samples with fluctuating predictions between training rounds, which are more likely to be near the decision boundary. This approach balances exploration and exploitation by adapting the sample selection strategy throughout the training process, minimizing inference costs while maintaining high selection effectiveness. Experimental results on benchmark datasets demonstrate that ACdSS outperforms existing FAL techniques, delivering superior accuracy with reduced annotation costs. This framework offers a practical solution for managing client heterogeneity in FAL and is well-suited for real-world federated learning systems, offering a significant reduction in computational overhead while improving model performance.
Referring Image Segmentation via Register-Aware Feature Selection and Adaptive Adaptation
Referring Image Segmentation (RIS) aims to segment target regions in an image at pixel level based on natural language descriptions. This paper proposes RAFS (Register-Aware Feature Selection and Adaptation), a parameter-efficient framework built upon DINOv3. Three lightweight adapter modules are designed: MLFS for adaptive multi-level feature aggregation via learnable Gaussian weighting, SCSA for efficient cross-modal fusion via depthwise separable convolutions and cross-modal attention, and RAFF for leveraging register tokens’ global context to enhance local features. With only 6.31M additional parameters, RAFS achieves competitive performance on RefCOCO, RefCOCO+, and G-Ref benchmarks.
Copyright (c) 2026 Xiaozhen Gao https://creativecommons.org/licenses/by-nc/4.0
Research on Urban Distribution Route Optimization Based on Time-Sliced OD Travel Time Matrices
Urban distribution operations are significantly affected by time-varying traffic conditions. If Euclidean distance or static shortest paths are still used as the travel cost between nodes, the actual distribution process under real road network conditions cannot be accurately represented. To address this issue, this study investigates a vehicle routing problem with soft time windows based on time-sliced travel times derived from a real road network. Travel time data between nodes in the core urban area of Zhengzhou are collected through an open map platform, and the service period is divided into multiple consecutive time intervals to construct time-sliced OD travel time matrices with directional and temporal heterogeneity. On this basis, a time-dependent vehicle routing optimization model is established with the objective of minimizing total distribution cost, in which time window deviations are incorporated into the objective function as penalty costs. Considering that local route adjustments may lead to subsequent changes in time states, an improved adaptive large neighborhood search algorithm is designed, together with a local time update mechanism to reduce repeated computations. A distribution network with 69 nodes in an urban area of Zhengzhou is used as the test instance, and the proposed method is compared with a genetic algorithm, ant colony optimization, simulated annealing, tabu search, and adaptive large neighborhood search. The results show that the proposed method can effectively reflect travel cost differences across time periods and achieves a relatively balanced performance in both total distribution cost control and computational efficiency.
Copyright (c) 2026 Zhiwei Tuo, Chengming Zhu https://creativecommons.org/licenses/by-nc/4.0
Research on Heterogeneous Transport Capacity Coordination Modeling and Comprehensive Evaluation for Large-Scale Earth-Moon Material Transfer Systems
Addressing the requirement to transport 100 million tons of materials for establishing a 100,000-person lunar settlement by 2050, this paper establishes a quantitative evaluation framework encompassing traditional rocket networks, pure space elevator systems, and hybrid transport solutions integrating both. The study first establishes a dynamic growth model based on technology learning curves, capturing the exponential enhancement of space elevator payload capacity over time. Simultaneously, for traditional rocket networks, a nonlinear decreasing model for per-launch costs with increasing reuse cycles is derived, incorporating reusability technology evolution trends. To achieve optimal allocation of transport resources during long-term construction phases, this study innovatively introduces a sigmoid function as a dynamic allocation weighting mechanism. This enables the system to fully leverage mature rocket technology during the initial construction phase while smoothly transitioning to the high-potential space elevator solution in the later stages. Quantitative evaluation using the Analytic Hierarchy Process (AHP) across two core dimensions—transportation time and comprehensive cost—reveals that the hybrid approach achieves a significantly superior composite score of 0.932 compared to pure rocket and pure elevator solutions. This study not only demonstrates the hybrid transport model's superiority in shortening project cycles and controlling long-term expenditures but also provides a scientific decision-making benchmark for strategic planning of large-scale deep-space logistics systems.
Copyright (c) 2026 Jinyu Zhang, Yifan Zhao https://creativecommons.org/licenses/by-nc/4.0
Synergistic Optimization of Competitive Performance and Commercial Profitability in Professional Women's Basketball
Addressing the operational challenge faced by professional women's basketball clubs in balancing competitive performance and commercial profitability under salary cap constraints, this study constructs an integrated multi-model dynamic decision-making system. Using the Connecticut Sun as a case study, the research first employs the Entropy Weighted Topix method to establish a player evaluation system encompassing competitive contribution, commercial value, and dynamic risk factors, enabling precise stratification of player value. Subsequently, a BP neural network is utilized for nonlinear forecasting of ticket, sponsorship, and merchandise revenues, combined with a Markov model to simulate the cross-seasonal evolution logic of team status. The core process employs multi-objective optimization using the NSGA-II algorithm to identify Pareto-optimal operational solutions, ensuring synergistic enhancement of competitive strength and economic returns while maintaining a 90.01% salary cap utilization rate. Addressing external uncertainties, the study quantifies potential financial risks from key player injuries and macroeconomic fluctuations via Monte Carlo simulations, while graph theory analyzes the win rate enhancement effects of team collaboration networks. Empirical results indicate that retaining the current 12 players yields an annual net profit of approximately $2.29 million and a projected 60% win rate under the baseline scenario. Through data-driven modeling, this study provides robust quantitative recommendations for resource allocation in professional sports.
Copyright (c) 2026 Haojun Jiang https://creativecommons.org/licenses/by-nc/4.0
Prediction of The Earliest Detection Time of Fetal DNA Concentration in Noninvasive Prenatal Testing Based on Multivariate and Logistic Regression Model
Fetal DNA concentration (FF) is a critical indicator affecting the accuracy and stability of non-invasive prenatal testing (NIPT). An excessively low FF may lead to test failure or false negatives. To address the lack of quantitative prediction for the earliest safe testing time at which clinical thresholds (FF ≥4%) are met, this study constructed multivariate linear regression and Logistic regression models based on publicly available sample data. The models analyzed the influence of gestational age and maternal body mass index (BMI) on FF levels and the probability of meeting the threshold, and introduced a gestational age quadratic term to establish a nonlinear model. The results demonstrated that BMI was a significant negative predictor of both FF and the probability of meeting the threshold. Further, the study derived the earliest gestational age at which the probability of meeting the threshold ≥95% for different BMI stratifications and validated model stability using the Bootstrap method. This research provides a quantitative basis for individualized NIPT testing timing.
Copyright (c) 2026 Jia Zhou, Huipeng Li https://creativecommons.org/licenses/by-nc/4.0
Optimization Study of Dual-Path Logistics Model for Interstellar Material Transport Integrating Space Elevators and Chemical Rockets
Addressing the extreme logistical challenge of transporting 100 million tons of materials across planets for the lunar colony construction mission launching in 2050, this paper establishes a dual-path logistics modeling framework integrating path deconstruction, parameter correction, and multi-objective optimization. The study categorizes transport routes into traditional rocket-based and space elevator-based modes. By introducing a geocorrection factor, it precisely quantifies the impact of different latitude launch sites on rocket payload capacity. Additionally, it derives the lunar soft-landing payload rate for space elevators using the Tsiolkovsky equation. At the optimization decision level, a nonlinear programming model balancing time and cost was established. Utilizing a heuristic algorithm based on a greedy strategy and grid search, the study compared the performance differences among pure rocket, pure elevator, and hybrid transport scenarios. To address real-world random uncertainties, disturbance terms such as equipment failures and maintenance costs were incorporated. The system's robustness was evaluated by constructing a set of near-optimal solutions. Simulation results confirm that the hybrid transport strategy optimally resolves the conflict between rockets' high initial costs and space elevators' limited early-stage capacity, achieving global benefit maximization under specific parameter constraints. This research provides a scientific quantitative basis and decision template for logistics planning in large-scale interstellar colonization.
Copyright (c) 2026 Bochen Tian, Shunqi Ji, Tianxiang Mo https://creativecommons.org/licenses/by-nc/4.0
Research on Transportation System Planning for Lunar Colonization Based on Pareto Optimization and Monte Carlo Simulation
Amid Earth’s worsening ecological pressure and resource conflicts, the Moon is humanity’s top choice for the first extraterrestrial colony. The 2050-launched 100,000-person lunar colony requires transporting 100 million tons of construction materials and securing long-term stable water supply. This paper builds a multi-model collaborative framework to evaluate lunar transportation schemes from cost, time, reliability and environmental impact perspectives. A weighted bi-objective optimization model for minimizing cost and time is constructed, and Pareto frontier analysis yields an optimal hybrid transportation ratio with a total cost of $1.08×10¹² and a 148.98-year duration. Monte Carlo simulation quantifies four failure scenarios’ impacts: rocket failures barely affect transportation time, while elevator and extreme failures cause severe delays and performance decline, requiring a 30-year buffer and a $221.4 billion contingency budget. Additionally, a regression forecasting-MOEA/D integrated framework estimates the colony’s annual water demand at 270,000 tons, verifying that elevator-dominated transportation is more economically efficient and operationally reliable for long-term lunar water supply.
Copyright (c) 2026 Haoyu Wang https://creativecommons.org/licenses/by-nc/4.0
A Training Strategy–Driven YOLOv11s Method for Traffic Sign Detection
Traffic sign detection is a fundamental component of intelligent transportation systems, where both detection accuracy and real-time performance are critical for practical deployment. Although deep learning–based object detectors, particularly single-stage YOLO-based methods, have achieved promising results in traffic sign detection, their performance remains limited when dealing with visually similar categories, small-sized targets, and complex traffic environments. Moreover, many existing approaches rely on architectural modifications or additional modules, which may increase model complexity and hinder real-time applicability. To address these challenges, this paper proposes a training-strategy-driven traffic sign detection method based on YOLOv11s, termed TS-YOLOv11s. Without modifying the original network architecture or loss function formulation, the proposed method improves detection performance by optimizing the training process. Specifically, loss weight adjustment is employed to enhance fine-grained category discrimination, label smoothing is introduced to mitigate overconfidence caused by limited samples, and data augmentation strategies tailored for small objects and complex scenes are applied to improve robustness and generalization. Extensive experiments conducted on the Chinese Traffic Sign Dataset demonstrate that the proposed method achieves high detection accuracy while maintaining real-time inference efficiency. The results indicate that TS-YOLOv11s provides an effective balance between performance and computational cost, highlighting the potential of training strategy optimization as a general and practical approach for traffic sign detection in real-world intelligent transportation systems.
Copyright (c) 2026 Zhuya Qi, Yiran Han, Gelin Zeng https://creativecommons.org/licenses/by-nc/4.0
Patent Value Score Prediction Based on BERT-XGBoost-Stacking with Late Fusion
Predicting the value scores of high-value patents is essential for evaluating technological innovation, managing intellectual property, and promoting industrial development. However, existing methods still face challenges in effectively fusing multimodal data and achieving high prediction accuracy. To address this issue, we propose a late fusion model based on BERT-XGBoost-Stacking to improve the accuracy and robustness of patent value assessment. This approach leverages BERT to extract deep semantic features from patent texts, employs XGBoost to model structured numerical features, and optimizes the fusion strategy through the Stacking framework. Experimental results on patents in China's new energy vehicle sector demonstrate that the proposed method outperforms single-modal models in terms of Mean Squared Error (MSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE), indicating higher prediction accuracy and stability. This study not only enriches quantitative methods for patent valuation but also provides new insights for the application of artificial intelligence in patent analysis, thereby supporting technological innovation and high-quality industrial development.
Copyright (c) 2026 Wenjuan Li https://creativecommons.org/licenses/by-nc/4.0
Research on a Lightweight and Efficient Vehicle Detection Approach Based on YOLO Algorithm
In recent years, intelligent transportation systems have developed rapidly, and autonomous driving systems, as key solutions to traditional traffic problems, have received increasing attention. Vehicle and pedestrian detection serves as a fundamental component within these systems. However, in practical application scenarios, it is challenging to achieve a good balance between algorithm accuracy and resource consumption; furthermore, accuracy degrades under complex conditions such as occlusion and illumination variations. To address these challenges, this paper proposes an efficient and lightweight vehicle and pedestrian detection model named YOLO-MDT, based on the YOLOv8n architecture. Firstly, we introduce a Feature Dynamic Task-Sharing Detection Head (DT-Head). This head reduces the number of parameters through weight sharing and enhances detection performance by facilitating feature interaction between classification and localization tasks. Secondly, we design a C2f-MEE module to replace the original C2f module. This new module improves multi-scale feature extraction and edge awareness capabilities, thereby boosting object detection performance. Finally, DySample upsampling and the Focal-PIoUv2 loss function are employed to replace the original upsampling method and loss function, respectively. This improves model convergence speed, enhances bounding box accuracy, and reduces computational overhead. The proposed model was validated on the SODA10M and KITTI datasets. It achieves a parameter count that is only 70% of the original network and reduces computational complexity by 0.1 GFLOPs. Significant improvements in mean Average Precision (mAP) were observed: mAP50 increased by 4.3% and 3.1%, while mAP50-95 increased by 2.9% and 3.2% on the SODA10M and KITTI datasets, respectively.
Copyright (c) 2026 Chengfeng Su, Qiang Xiang https://creativecommons.org/licenses/by-nc/4.0
Development and Empirical Study of an Intelligent Car's Line-Following and Obstacle-Avoiding Control System Based on the STC89C52 Microcontroller
With the development of the electronics industry, intelligent small vehicles not only have been widely used in industrial intelligence, but also the products used in smart homes are increasingly favored by people. This group's design is an intelligent small vehicle based on STC89C52. It uses an infrared sensor module for tracking and an ultrasonic sensor module for obstacle avoidance, and transmits the measured data to the embedded microcontroller. The single-chip microcontroller processes the data and gives responses to control the operation of the motor to achieve the functions of tracking and obstacle avoidance. This automatic tracking and obstacle avoidance intelligent small vehicle uses the STC89C52 single-chip microcontroller as the microprocessor, adopts the TCRT5000 infrared sensor module for infrared tracking, adopts the HC-SR04 ultrasonic sensor module for ultrasonic obstacle avoidance, uses the L298N motor driver board and two DC speed motors to form the motor drive module, and uses four South Power batteries to form the power circu. This automatic tracking and obstacle avoidance intelligent small vehicle uses the STC89C52 single-chip microcontroller as the microprocessor, adopts the TCRT5000 infrared sensor module for infrared tracking, adopts the HC-SR04 ultrasonic sensor module for ultrasonic obstacle avoidance, uses the L298N motor driver board and two DC speed motors to form the motor drive module, and uses four South Power batteries to form the power circuit. Through experiments, the intelligent car can successfully follow black lines and avoid obstacles within a 20cm range, achieving the expected design goals.
Copyright (c) 2026 Gang Qin, Yan Pan https://creativecommons.org/licenses/by-nc/4.0
PF-LSTM Reinforcement Learning Enhanced Hybrid Acoustic-Optical Adaptive Collaborative AUV Localization Algorithm
Cooperative localization of autonomous underwater vehicles (AUVs) is widely used in fields such as ocean exploration and environmental monitoring. However, its effectiveness highly depends on precise position estimation and clock synchronization mechanisms. Clock offset and drift, signal multipath attenuation, and dynamic interference in the underwater medium significantly constrain localization accuracy in anchor-free environments. Although existing cooperative algorithms have proposed solutions like TDOA/TDOC to address asynchrony, they still face challenges such as error accumulation, slow convergence, and energy consumption imbalance. To this end, this paper proposes a Potential Field-LSTM reinforced hybrid acoustic-optical adaptive AUV cooperative localization algorithm (PF-LSTM-QHAACL). The algorithm introduces a reinforcement learning decision framework incorporating Potential Field-based dense reward and LSTM temporal memory modules, thereby accelerating the learning process and improving localization accuracy. Simultaneously, to tackle clock asynchrony dynamics and acoustic-optical channel fluctuations, PF-LSTM-QHAACL employs a DQN-like mode switching mechanism for real-time channel assessment and adaptive training, further optimizing system stability and energy utilization. Furthermore, the algorithm integrates a hybrid ranging strategy combining Time Difference of Arrival (TDOA) and Received Signal Strength (RSS), effectively suppressing the impact of asynchronous bias on position estimation. Simulation results demonstrate that the PF-LSTM-QHAACL algorithm significantly enhances underwater localization accuracy and success rate in highly asynchronous scenarios.
Copyright (c) 2026 Qiankun Fu https://creativecommons.org/licenses/by-nc/4.0
Research on Power Generation Forecasting for Photovoltaic Power Plants Based on Spatio-Temporal Multidimensional Feature Decomposition and Deep Learning Architecture
Against the backdrop of energy transition driven by the “dual carbon” goals, this study addresses the challenges posed by the fluctuating power output of photovoltaic (PV) generation to grid stability by establishing an integrated forecasting framework combining physical modeling and deep learning. First, a theoretical irradiation and power generation model based on geographic location information was established as an ideal benchmark for deviation analysis. The STL decomposition method was applied to decompose the power sequence into seasonal, trend, and random components, while the K-means clustering algorithm quantified intraday power fluctuation characteristics. Analysis reveals a 55.30% deviation rate between actual and theoretical summer power, highlighting environmental uncertainty impacts. Subsequently, a “month-day-hour” three-dimensional tensor-based data reconstruction technique was introduced. By characterizing multi-scale features through seasonal indices and intraday distribution factors, the performance of LSTM and Transformer models in day-ahead power forecasting was comparatively validated. Experimental results demonstrate that the LSTM model exhibits significant advantages in capturing power variation trends, achieving a low root mean square error of 3.7229%. This effectively addresses the technical challenge of low prediction accuracy under complex meteorological conditions, providing reliable data support for grid dispatch.
Copyright (c) 2026 Yan Pan, Gang Qin https://creativecommons.org/licenses/by-nc/4.0
Cryptocurrency Market Behavior: A Data Analytics Approach to Price Prediction
With the rapid development of digital finance, cryptocurrencies have become an important component of the global financial market, and their price prediction has become a research hotspot with both theoretical and practical value. The high volatility, non-linearity and multi-factor driving characteristics of cryptocurrency prices make traditional financial prediction models difficult to achieve satisfactory results. This paper focuses on the research of cryptocurrency price prediction based on data analytics methods: first, it analyzes the multi-dimensional influencing factors of cryptocurrency market behavior, including on-chain data, macroeconomic indicators and social sentiment signals; second, it sorts out the application of mainstream data analytics models in price prediction, such as time series analysis, machine learning and deep learning algorithms; finally, it discusses the technical challenges faced by current prediction research, such as data noise interference and market black swan events, and proposes future optimization directions combined with emerging technologies such as federated learning and graph neural networks. This paper provides a systematic methodological framework for the research of cryptocurrency price prediction and the risk management of digital asset investment.
Copyright (c) 2026 Jiayu Zhang https://creativecommons.org/licenses/by-nc/4.0
Research on Intelligent Detection of Container Surface Damage Based on Deep Residual Networks
Addressing the issues of low efficiency and high subjectivity in container damage detection during automated port operations, this study employs deep residual networks to construct a high-precision system for determining the presence or absence of container damage. Based on a dataset of 3,713 images, the approach achieves the goal of extracting key damage features from complex port backgrounds by converting original YOLO annotations into binary classification labels. Targeted data augmentation strategies, including geometric and illumination transformations, were employed to address challenges such as reflections, shadows, and multi-scale damage in real-world scenarios. The model architecture incorporates three residual blocks, global average pooling, and a Sigmoid output layer, with skip connections effectively mitigating gradient vanishing during deep training. Experiments employed 3-fold hierarchical cross-validation and ensemble learning strategies, incorporating label smoothing and early stopping mechanisms to optimize training. Results demonstrate the model achieves 99.39% accuracy, 100% precision, and 99.39% recall on the validation set, while maintaining only 2.81 million parameters. This significantly enhances detection robustness and stability, providing reliable technical support for smart port development.
Copyright (c) 2026 Haoyang Zhu https://creativecommons.org/licenses/by-nc/4.0
Group Theory and Patterns Generation in High Order Rubik Cubes
This paper explores the relationship between group theory and Rubik’s Cube operations and explains how mathematical structures can be used to generate patterns on higher-order cubes. The operations of a Rubik’s Cube can be modeled by a finite permutation group, where each move corresponds to a permutation of edge and corner blocks. By analyzing the locations and orientations of these blocks, the paper explains why repeated operations eventually return the cube to its original state. The total number of valid configurations of a 3×3×3 Rubik’s Cube is derived using permutation constraints on edge and corner positions and orientations. Examples such as the operations U, RRUU, and FR are used to illustrate how permutation cycles determine the order of operations and the resulting cube patterns. The study further extends these ideas to higher-order cubes and demonstrates methods for generating visual patterns on a 7×7×7 cube using structured sequences of layer rotations.
Copyright (c) 2026 Qiyuan Sun https://creativecommons.org/licenses/by-nc/4.0
Design and Implementation of Low-Power IoT Edge Node for Precision Agriculture Based on ESP8266
Amid escalating resource management challenges, Smart Agriculture necessitates robust, energy-efficient monitoring solutions. However, traditional IoT nodes frequently struggle with excessive power consumption and unstable transmission in complex field environments. To overcome these bottlenecks, this paper presents a "Minimum Viable Unit" (MVU) edge node tailored for precision agriculture, integrating the ESP8266 controller with the industrial-grade CP2102 bridge. The proposed architecture employs a three-stage sleep strategy to dynamically optimize power usage and ensures stability under fluctuating supply voltages. Furthermore, the lightweight MQTT protocol is utilized to minimize bandwidth overhead and latency. Experimental results demonstrate that the deep-sleep current is successfully suppressed to 20μA, theoretically supporting over six months of autonomous operation on a standard lithium battery. In terms of reliability, the node maintains a packet loss rate below 0.5% even under indoor obstructed conditions (25 meters with wall penetration). This design offers a rigorous, verified hardware foundation for scalable, maintenance-free agricultural sensing networks.
Copyright (c) 2026 Bowen Zhao https://creativecommons.org/licenses/by-nc/4.0
Deep Learning-Based Low-Light Image Enhancement: A Review
With the rapid development of deep learning in the field of computer vision, low-light image enhancement (LLIE) has shifted from traditional handcrafted prior-based methods to data-driven learning paradigms. Deep models can automatically learn the complex non-linear mapping between low-light and normal-exposure images through end-to-end training, showing remarkable advantages in brightness improvement, detail restoration, and noise suppression. According to the dependence on labeled data and the form of supervision signals during training, existing deep learning-based LLIE methods are mainly divided into five categories: supervised, reinforcement, unsupervised, zero-shot, and semi-supervised learning. Among them, supervised learning is the most mature and mainstream technical route, which has evolved from convolutional neural networks and Retinex decomposition to Transformer and state-space models (e.g., Mamba), achieving accurate recovery of illumination, texture, and color with stable performance. Reinforcement learning formulates LLIE as a sequential decision-making problem but is still in the exploratory stage due to low learning efficiency and high sensitivity to reward function design. Unsupervised and zero-shot learning methods solve the problem of difficult data annotation in real scenarios by designing unpaired, no-reference, or self-supervised mechanisms, respectively. Semi-supervised learning balances data acquisition cost and enhancement performance by combining a small amount of labeled data with a large number of unlabeled data. This paper summarizes the core principles, representative works, advantages, and existing challenges of various methods, pointing out that supervised learning dominates LLIE due to its stability and precision, while other methods provide effective supplements in data-scarce or complex scenarios. Future research should focus on improving the adaptability of models to different signal-to-noise ratio regions and balancing global illumination consistency and high-frequency detail preservation.
Copyright (c) 2026 Pengyun Shi https://creativecommons.org/licenses/by-nc/4.0
Mechanism of n-Hexane Insolubles in Biomass-Coal Co-Pyrolysis and Optimization of Their Mixing Ratios
This study thoroughly investigates the influence mechanism of n-hexane insolubles (INS) and their blending ratio on product yields during the co-pyrolysis of biomass and coal. First, Spearman's correlation coefficient analysis revealed intrinsic relationships between INS content and yields of tar, water, and char. Results indicate significant correlations between INS and tar/char yields, while its effect on water yield is negligible. Subsequently, to further elucidate yield variation patterns under complex operating conditions, variance analysis was employed to investigate the interactive effects of INS and blending ratios on product yields. Findings revealed that different INS-blend combinations significantly altered tar growth rates and coke residue decline trends. Building upon these findings, a nonlinear optimization model was constructed to maximize energy conversion efficiency and product utilization. The Sequential Quadratic Programming (SLSQP) algorithm was employed to identify optimal blending ratios and INS dosage under specified cost and technical constraints. The research outcomes provide scientific theoretical foundations and operational guidance for optimizing biomass energy utilization, enhancing energy efficiency, and achieving sustainable energy production.
Copyright (c) 2026 Xiaoyu Liu https://creativecommons.org/licenses/by-nc/4.0
Dual-Cloud Collaborative Graph Edit Distance Secure Computation Protocol
To address the challenge of securely computing graph edit distance in directed graph scenarios without compromising parties' privacy data, this paper proposes a homomorphic encryption-based, dual-cloud-assisted secure graph edit distance computation protocol. The protocol encodes graph structures as adjacency matrices and introduces random parity noise to protect the original data's parity. It then leverages homomorphic encryption to compute edit distance in ciphertext form. Employing a dual-cloud server architecture, the protocol offloads most computational tasks to the cloud, eliminating direct interaction between data users. This approach enhances computational efficiency while ensuring privacy security. Theoretical analysis and simulation experiments demonstrate the protocol's security under a semi-honest model, with superior user-side computational overhead compared to existing solutions.
Copyright (c) 2026 Yufeng Wang https://creativecommons.org/licenses/by-nc/4.0
LED Light Source Based on Adjustable Biological Rhythms
In this paper, the whole process technology system of health lighting is constructed: a spectral parameter calculation system based on CIE standards is established, and the core parameters such as XYZ triple stimulus value, CCT, and mel-DER are accurately calculated through numerical integration, Krystek segmented fitting, Gaussian simulation, etc. A multi-channel LED multi-objective collaborative optimization framework and a solar spectral time-varying dynamic regulation model are constructed, and the objective function of optical characteristics and circadian rhythm design is integrated, and the SLSQP algorithm, time smoothing constraint and intelligent initialization strategy are introduced to ensure the optimization effect. The core performance is verified by experiments: high color rendering ( ) and low rhythm interference (mel-DER=0.2761) with a single light source, dual mode to achieve day and night color temperature switching, and the dynamic model accurately reproduces natural light. Research innovation provides solutions from single-source evaluation to full-day dynamic simulation, providing quantitative support for health lighting design, and its linear assumptions and sample size limitations need to be further improved.
Copyright (c) 2026 Binghao Li https://creativecommons.org/licenses/by-nc/4.0
A Multiple Regression-Based Method for NIPT Timing Selection and Fetal Abnormality Detection
Non-invasive prenatal testing (NIPT) is a widely applied clinical technique for detecting fetal chromosomal abnormalities by analyzing cell-free fetal DNA fragments in maternal plasma. The accuracy and reliability of NIPT are affected by multiple factors, including gestational age and maternal body mass index (BMI). This paper investigates the correlation between Y chromosome concentration, gestational weeks, and BMI in male fetuses, as well as the feasibility of predicting female fetal abnormalities in the absence of Y chromosome signals. To address these issues, this article establish a comprehensive framework combining interaction regression analysis, gradient boosting decision trees (GBDT), rule-based grouping, random forests, and logistic regression models. Based on historical data, optimal NIPT time points are estimated for different BMI groups by calculating the gestational weeks at which 95% of pregnant[1] women achieve the required fetal DNA concentration, with additional safety margins introduced to enhance robustness. Experimental results show that the optimal testing window for male fetuses is approximately 11 ± 3 weeks, while the proposed model achieves a precision of 0.8178 and a recall of 0.8621 for female fetal abnormality detection. The findings provide practical clinical recommendations to minimize potential testing risks, improve detection success rates across maternal BMI groups, and offer effective judgment methods for female fetuses lacking Y chromosome markers.
Research on small object detection method based on YOLOv8:Application of high-resolution detection layer and Mosaic data augmentation
For the core problem that the number of small targets in remote sensing images is continually increasing and traditional object detection methods struggle to meet its detection requirements, a small-target detection method based on YOLOv8 is proposed, and its detection performance is enhanced through two key improvements. First, to address the difficulty of detecting small targets, a high-resolution detection layer P2 is added to the Neck part of the YOLOv8 model to enhance the model's feature extraction capability for small targets. Secondly, the Mosaic data augmentation technique is introduced, which stitches multiple images into one image to expand the diversity of training data, thereby improving the model's generalization to small targets. Experiments on the NWPU VHR-10 dataset show that the improved YOLOv8 model significantly outperforms the original model in small-target detection.Specifically, the Recall rate of the improved model reaches 85.6%, which is 9.18% higher than that of the baseline model. At the same time, mAP@0.5 edged up to 0.724, while the more stringent mAP@0.5:0.95 index increased significantly from 0.491 to 0.514.These results validate the effectiveness of the proposed approach in improving small-target detection performance.
A Review of Applications and Research Advances of Large Models in OCR Technology
Optical Character Recognition (OCR) is a key technology for document digitization and textual information extraction. However, traditional methods are often limited by practical challenges such as font diversity, complex layouts, and image degradation. In response, this paper provides a systematic review of recent advances in OCR driven by large models. First, a review framework of “bottleneck analysis – technical response – performance evaluation” is constructed, and the paradigm shift is examined from three dimensions: model architecture, training paradigms, and application scenarios. Within this framework, we systematically categorize and compare three mainstream technical approaches: cross-modal pre-trained models, end-to-end sequence generation methods, and few-shot/zero-shot adaptation techniques. Then, through a comparative analysis of representative models in terms of accuracy, robustness, and efficiency, we highlight the significant advantages of large models in complex document understanding, natural scene text recognition, and multilingual generalization, while also noting their persistent limitations in computational cost, hallucination suppression, and domain-specific adaptation. Finally, by considering emerging trends like lightweight deployment, multimodal fusion, and privacy-preserving computation, the paper envisions OCR evolving toward an efficient, adaptive, and cognitively-enabled new paradigm, thereby providing a roadmap for future research and practice.
MapReduce Word Frequency Statistics Based on Serverless Platform
In the past few years, people’s demand of speed and efficiency in extracting information has increased dramatically, which gives rise to the surge in the demand of text data processing. Traditional distributed computing framework based on VMs are limited by some inherent defects such as wasting resource reservation, large overhead, rigid scaling, which further cause bad utilization and poor performance when running on burst workloads. This paper design and implement a Serverless MR system on Alibaba Cloud Function Compute (FC) and Object Storage Service (OSS). The Map and Reduce part is split into independent and event-driven functions, and then automatically executed and allocated across FC instances. The experiment results on text word frequency counting show that the system is efficient in elasticity and cost. Especially, it’s efficient in lightweight applications with high concurrency and transient workloads. This work provides an efficient and manageable big data processing platform for small and medium teams. Meanwhile, it also provides an example of how to apply Serverless computing in distributed processing model.
A Data-Driven and Experience-Driven Iterative Design Method for Intelligent Products
To address the insufficient integration of data and experience-driven approaches in the iteration of intelligent products, this study designs an original DECI algorithm, constructs an integrated iterative design framework, and conducts experimental verification. The DECI algorithm achieves subjective experience quantification and dynamic dual-modal collaboration through three innovations: an experience intent embedding module, an adaptive dynamic weighting mechanism, and a closed-loop iterative update strategy, overcoming the limitations of static fusion. A four-layer progressive framework is built, covering data acquisition, feature processing, fusion iteration, and effect output layers, opening up the dual-modal fusion path and forming a closed-loop iterative chain throughout the entire process. Using intelligent office software and mobile service apps as examples, multi-dimensional experiments were conducted with three comparative algorithms. The results show that the DECI algorithm reduces response time and error rate by 10.1%-40.5% compared to the best comparative algorithm, increases user satisfaction by 4.8%-23.4%, shortens the iteration cycle by 16.1%-23.9%, and controls performance fluctuation in high-concurrency scenarios within 2.1%, with all differences being statistically significant. This study constructs an iterative scheme that balances quantitative accuracy and subjective experience, providing theoretical support and an engineering paradigm for the efficient iteration of intelligent products.