This investigation aims to explore users’ accuracy in identifying computer mice designed with the golden ratio and their aesthetic preferences, with a specific focus on gender differences. First, the study used a database of 233 Genius brand mice and selected five samples with length-to-width ratios ranging from 1.42 to 1.78. A total of 99 university students (62 females and 37 males) participated in absolute and relative judgment tests. Results showed that most participants failed to correctly identify the mouse with a ratio closest to the golden ratio (approximately 1:1.62), even when provided with 2D or 3D visual references. The chi-square test showed that the difference in recognition accuracy between males (32%) and females (34%) was not statistically significant (p = 0.34). In addition, there was no correlation between aesthetic preference and whether the mouse followed the golden ratio. These findings suggest that golden ratio design is neither easily recognizable nor a key factor in product preference, and designers need not overly rely on it to enhance product appeal. Finally, polynomial regression analysis was employed to investigate the effect of the ratio on the preferences of all participants. The model fit was very high (R 2 = 99.91%, p-value = 0.038), showing that the mouse ratio was associated with all participants’ preferences. According to the results, if a ratio/preference prediction system for mouse design is developed in the future, a mouse design with an aspect ratio of 1.5 to 1.56 can serve as an important reference indicator for preference prediction.

Context: Increasing climatic variability threatens the efficacy of conventional water treatment lines, particularly gravity filtration, a robust and economically accessible process in resource-limited contexts. Lake Kabongo, a major supply source, exhibits significant quality fluctuations (turbidity, organic matter, algal blooms) likely to alter filter performance.  Objective: To develop a hybrid (mechanistic–statistical) predictive model of gravity filtration performance (effluent turbidity, head loss, cycle duration) based on raw water quality, to shift from empirical operation to anticipatory management.  Methodology: A systematic meta-analysis of over twenty historical trials conducted between May and June 2025 on Lake Kabongo water was performed. A hybrid model combining fundamental equations of porous media filtration and multivariate polynomial regressions calibrated on experimental data was developed. Validation is based on data partitioning (70/30), comprehensive statistical analysis (coefficients with 95% CI, residual analysis) and simulation of extreme climatic scenarios.  Key Results: Initial turbidity, Total Organic Carbon (TOC) concentration and UV275 absorbance explain over 85% of the performance variance. The final model shows coefficients of determination of 0.89 for effluent turbidity, 0.86 for TOC and 0.83 for UV275. Sensitivity analysis identifies activated carbon height (Hc) as the second most influential parameter after initial turbidity. Simulations reveal critical thresholds (e.g., turbidity > 100 NTU) beyond which filtration efficiency drops sharply.  Conclusion / Scope: The developed tool allows for optimization of the future Katebi containerized plant operation by anticipating at-risk periods and adjusting operational parameters. This approach is transferable to other gravity filtration systems subject to hydro-climatic variability and contributes to securing drinking water production in a context of global change.

In this study, we show the quantitative structure-property relationship (QSPR) for amphetamine derivatives based on neighborhood degree-based topological indices and NM-polynomials. By coupling such descriptors to both polynomial regression models and Random Forest algorithms, the ability of these two methodologies to predict different physicochemical properties (boiling point, evaporation energy, flash point, molar refractivity, surface tension, polarizability and SA) is analyzed. The modeling scheme reveals that the neighborhood-based indices carry information specific to structural complexity, connectivity and electronic characteristics important for stimulant-type molecules behaviour. cubic regression models are also found to be more capable of representing nonlinear structural relationship than quadratic ones while the efficacy and generalizability are greatly improved by extra Random Forest in particular for properties with strong dependence on molecular branching and electronic distribution. In conclusion, the results here presented confirm that NM-polynomial based descriptors effectively relate molecular topology with experimentally measurable physicochemical behavior, thus suggesting their computational use in predictive property modeling, early drug screening and cheminformatics-driven design.

To develop and validate a deep learning (DL)-based algorithm for automated measurement of femoral head ossification center (FHOC) size and establish AI-derived growth charts. This retrospective study included 1705 healthy Korean children (mean age, 5.1 ± 3.3 years; 841 females, 864 males) with anteroposterior pelvic radiographs (2018-2024). A three-stage DL algorithm (region-of-interest detection, FHOC segmentation, landmark-based size computation) was used to automatically measure FHOC size. Agreement with radiologist measurements was evaluated using concordance correlation coefficient (CCC), Pearson correlation coefficient (r), mean absolute error (MAE), root mean square error (RMSE), and Bland-Altman analyses, supplemented by paired t-test and Fisher's Z-test. AI measurements were used to create FHOC growth charts via quantile polynomial regression, with predictive accuracy assessed by adjusted R², MAE, and RMSE. AI-derived FHOC size measurements showed close agreement with radiologist measurements, with mean differences within ±0.5 mm and 95% limits of agreement within ±3 mm in age-stratified analyses, and overall agreement was further supported by high CCC, r, and consistently low error metrics. Growth curves based on AI measurements demonstrated strong predictive accuracy (adjusted R² = 0.927 for females; 0.934 for males), with low errors across age groups (females: MAE 1.77-2.98 mm, RMSE 2.28-3.54 mm; males: MAE 1.60-3.01 mm, RMSE 2.00-4.10 mm). Reference percentiles (5th-95th) were established, providing standardized FHOC size ranges for clinical application. Our DL-based approach provides precise and reproducible FHOC size measurement, offering a robust reference for standardized growth assessment and early pediatric hip joint evaluation. QuestionThe timing of FHOC appearance is an important radiographic indicator; however, manual measurement is subjective, and studies on age-specific changes remain limited. FindingsA DL-based algorithm achieved high agreement with expert measurements, and age-based regression reliably predicted FHOC size in children. Clinical relevanceAI-derived FHOC growth charts may provide objective, standardized references for pediatric hip joint development, potentially enabling earlier detection of growth abnormalities and improving diagnostic consistency in clinical practice.

Abstract This study investigated the diffusion of leaked liquefied petroleum gas (LPG) and analyzed the load distribution characteristics of a petrochemical control room under a vapor cloud explosion (VCE) flow field based on the ANSYS/Fluent software. The results showed that the leaked LPG tended to accumulate near the ground. High wind speed accelerated the propagation of the leaked LPG cloud along the leaked direction and accelerated the dilution of the leaked LPG in the side direction. Besides, the existence of obstacles can significantly increase the gas cloud concentration near the obstacles. The nonuniform concentration field generated by leakage accidents can initiate detonation with relatively low ignition energy. In sparsely obstructed environments, the explosive behavior followed the classic open‐space gas cloud explosion pattern, where peak overpressure decreased with distance. The peak overpressure during explosions increased markedly with more obstacles, demonstrating that complex obstructions substantially elevated the risk of explosion accidents. The load distribution across control room walls exhibits significant nonuniformity in both temporal and spatial dimensions. The statistical analysis on historical maximum load distributions at different wall positions was conducted, employing bivariate quadratic polynomial fitting to derive a simplified calculation formula, which can be applied to analyze load distribution patterns across control room walls.

Finding a job that fits is widely recognized as important for personal fulfillment and professional success. Despite the long history of person-environment fit research, surprisingly little is known about person-job fit in terms of basic personality traits. This study examined three basic tenets of fit theory regarding personality-job fit: Fit (1) is pleasurable, (2) regulated by individuals, and (3) changes over time. We hypothesized that personality-job fit would be associated with higher subjective well-being (RQ1), predict less occupational change (RQ2), and vary across the professional lifespan (RQ3). Fit was conceptualized as “broad congruence” between individuals’ Big Five trait levels and expert-rated trait demands of their occupations. We used nationally representative data from German jobholders ( N = 18,712–30,883). Multilevel polynomial regression and response surface analysis showed no significant congruence effects but some interactions: More extraverted and open individuals felt better and were less likely to leave their jobs when these traits were strongly demanded by their work, though these outcomes were not optimized at exact personality-job fit. Additionally, personality-job fit improved over time, showing a linear increase across the lifespan. These findings emphasize studying fit theories in detail and considering individuals’ personalities, such as being communicative or original, in career choice.

BackgroundIdentifying evolving antimicrobial resistance patterns is essential for public health, stewardship, and infection control. The veteran spinal cord injury (SCI) population is particularly vulnerable, facing antibiotic pressure from recurrent urinary tract infections and treatment of asymptomatic bacteriuria— both drivers of resistance. We characterized 24-year temporal and regional trends in antimicrobial resistance among urinary pathogens in SCI patients across the U.S. Veterans Affairs.Temporal and Regional Trends in ESBL-Producing Enterobacterales Among SCI Patients — United States, 1999–2023VISN-level incidence rates of Enterobacterales with an ESBL phenotype are expressed per 100 person-years and displayed as 5-year choropleth maps. National incidence rates per 1,000 population are shown as an annual trend line smoothed using second-degree polynomial regression. A clockwise geographic spread was observed, originating in the Midwest and Northeast and extending to the South and Southwest, with persistently elevated rates along this trajectory. National rates increased through 2015 before plateauing.Temporal and Regional Trends in ESBL-Producing Pseudomonas aeruginosa Among SCI Patients — United States, 1999–2023VISN-level incidence rates of Pseudomonas aeruginosa with an ESBL phenotype are expressed per 100 person-years and displayed as 5-year choropleth maps. National incidence rates per 1,000 population are shown as an annual trend line smoothed using second-degree polynomial regression. Unlike Enterobacterales, no clear geographic shift was observed; however, resistance remained widespread, with relatively higher incidence in the Midwest, Northeast, South, and Southwest. National rates steadily declined over time.MethodsWe conducted a retrospective cohort study of urine cultures from SCI patients across 1,380 VA facilities from 1999 to 2023. Positive cultures for Enterobacterales (Escherichia coli and Klebsiella pneumoniae) and Pseudomonas aeruginosa were identified. Extended-spectrum beta-lactamase (ESBL) phenotype and carbapenem resistance (CR) were defined according to Clinical and Laboratory Standards Institute susceptibility criteria. Incidence rates were calculated per 100 person-years, stratified by Veterans Integrated Service Networks (VISNs) in 5-year intervals, and visualized using choropleth maps. National trends were modeled using second-degree polynomial regression to capture non-linear incidence patterns.Temporal and Regional Trends in Carbapenem-Resistant Enterobacterales Among SCI Patients — United States, 1999–2023VISN-level incidence rates of carbapenem-resistant Enterobacterales are expressed per 100 person-years and displayed as 5-year choropleth maps. National incidence rates per 1,000 population are shown as an annual trend line smoothed using second-degree polynomial regression. Resistance demonstrated a clockwise geographic shift, with the South and Southwest—particularly VISNs 8, 16, 17, and 22—emerging as recent hotspots. The national trend peaked around 2015 before beginning to decline.Temporal and Regional Trends in Carbapenem-Resistant Pseudomonas aeruginosa Among SCI Patients — United States, 1999–2023VISN-level incidence rates of carbapenem-resistant Pseudomonas are expressed per 100 person-years and displayed as 5-year choropleth maps. National incidence rates per 1,000 population are shown as an annual trend line smoothed using second-degree polynomial regression. Resistance was widespread, with greater density in the Midwest, Northeast, and South; VISN 12 remained consistently elevated across all intervals. The national trend showed a gradual decline over time.ResultsWe identified 49,326 SCI patients who contributed 302,495 unique urine cultures over 24 years. Resistance patterns evolved more consistently by organism than by phenotype. Enterobacterales showed increasing national incidence through 2015 followed by plateauing, with a clockwise geographic spread beginning in the Midwest and Northeast, extending to the South and Southwest, and leaving a lasting pattern of elevated resistance along the way. In contrast, P. aeruginosa showed a steady national decline in resistance, with no clear geographic shift but widespread distribution and persistently higher incidence in the Midwest, Northeast, South, and Southwest. VISN 12 was an early and persistent hotspot for resistance.ConclusionEnterobacterales showed rising resistance with a notable geographic shift toward the South and Southwest. In contrast, P. aeruginosa demonstrated continued national declines persistently widespread distribution. These shifts may reflect stewardship efforts, patient movement, or other external pressures.DisclosuresAll Authors: No reported disclosures

The study addresses the problem of forecasting the electrical load of an energy facility under conditions of high consumption variability. A comparative analysis of forecasting model performance is carried out for horizons of 1 and 24 hours. For the first case, the SSA, Holt–Winters methods, as well as LSTM and Transformer neural network architectures, were examined. For the second case, models with prior decomposition based on the Hilbert–Huang transform (model M1) and polynomial regression (model M2) were additionally considered. The quality of the models was evaluated using four metrics: mean error (ME), mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE). The results show that, for the 1-hour horizon, the Transformer model achieved the lowest MAE and MAPE values (2.54 kW and 4.95%, respectively), indicating high accuracy. LSTM demonstrated similar accuracy, with the smallest forecast bias. The SSA and Holt–Winters models were significantly less accurate, though they showed better stability in avoiding large errors. For the 24-hour horizon, the Transformer model achieved the best results in both accuracy and stability (MAE = 3.61 kW). The M1 model, based on the Hilbert–Huang transform, showed balanced performance across all metrics, while LSTM achieved high absolute accuracy. Additional analysis of mean error distribution frequencies showed that Transformer and LSTM provide high densities of accurate forecasts within narrow error intervals, unlike SSA and Holt–Winters, which are characterized by systematic biases. The conclusions have practical significance for energy management tasks in microgrid conditions, particularly for operational load planning, loss reduction, and optimization of backup power sources. References 16, figures 2, tables 3.

This study evaluated the effects of dietary methionine (Met) levels on the growth performance of Pekin ducks and estimated their Met requirements during the starter (1 to 14 days; Exp. 1) and grower (15 to 35 days; Exp. 2) phases. In Exp. 1, 288 one-day-old male ducklings were randomly assigned to six diets containing analyzed Met levels of 0.291%, 0.343%, 0.392%, 0.438%, 0.483%, and 0.521% (six replicates; eight birds each). In Exp. 2, 150 ducks at 15 days of age were allocated to five diets with analyzed Met levels of 0.271%, 0.342%, 0.421%, 0.501%, and 0.566% (six replicates; five birds each). Growth performance was recorded in both experiments, and Met requirements were estimated using linear broken-line and quadratic polynomial models. During the starter phase, increasing Met intake resulted in linear and quadratic improvements in weight gain and a linear reduction in feed/gain (F/G). For the grower phase, weight gain showed a quadratic response, with the highest gain at 0.421% Met, while F/G decreased linearly and quadratically. Estimated Met requirements for the starter phase were 0.404% (linear broken-line) and 0.532% (quadratic polynomial), and for the grower phase were 0.371% and 0.473%, respectively. Using the intercept of the two models, recommended Met levels were 0.455% for starter ducks and 0.411% for growing ducks. These integrative values likely provide more practical and economically relevant recommendations than relying on a single model, as broken-line analysis may underestimate and quadratic models may overestimate actual nutrient requirements.

Excavation of ultra-shallow pilot tunnels triggers surface settlement and endangers surrounding pipelines. The discontinuous settlement curve from traditional stochastic medium theory cannot be directly integrated into the foundation beam model, limiting pipeline deformation prediction accuracy. The key novelty of this study lies in proposing an improved coupled method tailored to ultra-shallow burial conditions: converting the discontinuous settlement solution into a continuous analytical one via polynomial fitting, embedding it into the Winkler elastic foundation beam model, and realizing pipeline settlement prediction by solving the deflection curve differential equation with the initial parameter method and boundary conditions. Four core factors affecting pipeline deformation are identified, with pilot tunnel size as the key. Shallower depth (especially 5.5 m) intensifies stratum disturbance; pipeline parameters (diameter, wall thickness, elastic modulus) significantly impact bending moment, while stratum elastic modulus has little effect on settlement. Verified by the Xueyuannanlu Station project of Beijing Rail Transit Line 13, theoretical and measured settlement trends are highly consistent, with core indicators meeting safety requirements (max theoretical/measured settlement: −10.9 mm/−8.6 mm < 30 mm; max rotation angle: −0.066° < 0.340°). Errors (max 5.1 mm) concentrate at the pipeline edge, and conservative theoretical values satisfy engineering safety evaluation demands.

General Background: Public sector budget planning requires data-driven approaches to support service sustainability, particularly for emergency institutions such as regional fire departments. Specific Background: The Minahasa Regency Fire Department budget planning has relied on historical allocations that exhibit fluctuating and non-linear trends across expenditure categories. Knowledge Gap: Previous planning practices have not fully utilized non-linear statistical modeling to interpret historical budget dynamics and medium-term projections. Aims: This study aims to analyze historical budget trends and predict expenditure needs for the 2025–2027 period using a second-order polynomial regression model. Results: Using budget data from 2019–2024, the model successfully captured non-linear expenditure patterns, including a sharp increase in personnel and capital expenditures in 2024, with coefficients of determination of 0.448 for personnel expenditures and 0.409 for capital expenditures, while total projected expenditures approach IDR six billion by 2027. Novelty: This research integrates second-order polynomial regression with an interactive Streamlit-based application for visualizing and interpreting public sector budget projections. Implications: The findings provide an analytical basis for local governments to anticipate medium-term budget requirements, prioritize expenditures, and strengthen data-based financial planning for fire service operations. Highlights • Second-order polynomial modeling captures non-linear expenditure patterns across budget categories• Historical personnel expenditure spikes shape medium-term fiscal projections• Streamlit-based visualization supports data-driven public budget planning Keywords Polynomial Regression; Budget Prediction; Fire Department; Historical Data; Streamlit Application

Artificial intelligence (AI) has revolutionized sports science, advancing performance analysis, injury prevention, and strategy optimization. However, its long-term impact remains underexplored. This study conducts a bibliometric and predictive analysis of -driven sports research over the past decade, identifying key contributors, emerging trends, and future directions through visualization techniques. Method: A systematic review was conducted on related sports research from 2014 to 2024 using the Web of Science Core Collection. Bibliometric tools Citespace and Vosviewer were employed to analyze publication trends, author networks, institutional collaborations, and keyword co-occurrences. Polynomial regression analysis was applied to forecast future research growth based on historical publication and citation trends. A total of 5,811 publications with 96,753 citations were identified. China, the United States, and the United Kingdom were the most productive countries, with China leading in volume but exhibiting lower citation impact. The Chinese Academy of Sciences, Stanford University, and the University of Oxford were the top research institutions. Keyword analysis revealed that "machine learning," "deep learning," and "computer vision" were the most studied topics, while emerging themes such as "stress analysis," "information processing," and "pose estimation" indicated shifts towards driven real-time monitoring and predictive analytics. Polynomial regression models predicted continued research growth, with publication trends following y = 354x ² + 1350x + 528 (r ² = 0.94) and citation growth modeled as y = 9680x ² + 24900x + 7850 (r ² = 0.99), suggesting sustained acceleration in AI applications within sports science. The integration of sports science has grown rapidly, with machine learning and computer vision playing a pivotal role in optimizing athletic performance, real-time feedback, and injury prevention. Predictive analytics and driven modeling can transform sports training by personalizing programs based on biomechanical and physiological data, enhancing both performance and injury resilience. However, disparities in AI adoption across regions and institutions highlight the need for greater international collaboration, particularly in developing regions where access to driven sports technologies is limited. Future research should refine -driven models for individualized training, integrate wearable sensor data for precision, and address ethical concerns. Additionally, policymakers and sports organizations should invest in AI-based training and health monitoring systems to bridge the gap between technology-rich and technology-limited regions. As it evolves, its role in sports science will expand, driving advancements in performance analysis, health monitoring, and strategic decision-making.

As a preprocessing step of spectroscopic techniques such as Raman spectroscopy, infrared spectroscopy, electrophoresis, etc., the baseline correction is very important for improving the signal quality, thereby ensuring the reliability and accuracy of the data analysis. Methods such as polynomial fitting, wavelet transforms, and frequency-domain filtering are widely used for baseline correction, effectively reducing interference and enhancing the reliability of signal analysis. However, these methods have certain limitations: (i) Polynomial fitting faces challenges in determining the optimal order, which may affect the fitting quality, (ii) wavelet transforms are complex and require fine adjustments, and (iii) frequency-domain filtering may cause signal distortion. These shortcomings affect the implementation of the algorithm in spectral related industries. Therefore, finding an appropriate algorithm to optimize baseline removal is crucial for the development of automated spectral analysis equipment. Here, we propose a rolling ball baseline removal algorithm based on morphological operations. With its simple implementation and excellent baseline removal performance, this method effectively avoids the overfitting problems. It is suitable for baseline correction in not only Raman spectroscopy, but also various other types of spectral data. In all, this approach offers a convenient and efficient general solution for the processing of various spectral data.

Lipid estimation of microalgae via Finite element simulation using voltage discharging technique.

Brazil is the world’s fifth largest milk producer, and Minas Gerais is the leading milk-producing state. Most of the state production comes from small and medium-sized family farms, and only a small number of cities have high productivity metrics. The current climate change scenario poses technical challenges to milk production, affecting the health and the productivity of the cattle. Here we evaluated dairy farming in Minas Gerais state, considering productivity and official climatic data. We analyzed official data from different government databases, and among the 853 cities, 12 were classified as high-production cities (>80,000 L/year), of which six had complete climatic records. Pompéu emerged as the top producer with high precipitation rates, whereas Patos de Minas showed the highest precipitation, with irregular distribution. Using quadratic polynomial regression, we found that precipitation significantly influenced production (R2=0.8993, p=0.0076). Temperature alone had a negligible effect (R2=0.1995, p=0.7174). Principal Component Analysis identified distinct climatic patterns among the cities, with January and December being the wettest periods. Notably, high-productivity areas maintained moderate temperatures (21–23°C) and lower animal densities (km2). Our data open doors for further investigation into the interplay between climatic changes and zootechnical parameters of interest in milk production.

Lipids are essential for crustacean reproduction, supporting broodstock growth and ovarian development. However, studies of n-3 highly unsaturated fatty acids (HUFAs), particularly eicosapentaenoic acid (EPA), on the growth and ovarian development of prawn broodstock remain limited. Accordingly, five experimental diets containing EPA concentrations of 0.12%, 0.79%, 1.46%, 2.21%, and 2.78% were formulated to examine their effects on ovarian development and broodstock health in the giant freshwater prawn Macrobrachium rosenbergii (initial weight: 9.32 ± 0.52 g) and to determine dietary EPA requirements during ovarian maturation. The results were as follows: (1) no significant differences in survival rate were observed among groups. Weight gain (WG) initially increased and then declined, reaching the highest values in the 1.46% EPA group, although differences among treatments were not significant. In contrast, hepatopancreas index decreased significantly with increasing dietary EPA (p < 0.05). (2) Dietary EPA significantly altered hepatopancreatic fatty acid composition. Saturated fatty acid (SFA) levels showed no significant differences, whereas monounsaturated fatty acids (MUFAs) decreased significantly (p < 0.05). In contrast, polyunsaturated fatty acids (PUFAs) and HUFA increased significantly with higher dietary EPA (p < 0.05), peaking in the 2.78% EPA group. (3) Antioxidant parameters, including total antioxidant capacity (T-AOC), total superoxide dismutase (T-SOD), and glutathione peroxidase (GSH-Px), followed a pattern of initial increase followed by decline with higher EPA levels (p < 0.05). Malondialdehyde (MDA) content showed the opposite trend, reaching its lowest level in the 1.46% EPA group (p < 0.05). (4) Ovarian histology revealed that the 1.46% EPA group exhibited a higher proportion of mature oocytes, with most females reaching ovarian development stages III-IV, and this group also showed the highest gonadosomatic index (GSI). Steroid hormone secretion was significantly affected by dietary EPA (p < 0.05). (5) At the molecular level, EPA inhibited the expression of genes related to lipid synthesis in the hepatopancreas (p < 0.05) and promoted fatty acid β-oxidation, but excessive EPA caused irreversible hepatopancreatic damage. Polynomial regression analysis of steroid hormone secretion indicated that 1.32% and 1.50% dietary EPA supported maximum progesterone (PROG) and 17β-estradiol (E2) levels, respectively. Overall, a dietary EPA level of 1.46% was found to promote broodstock growth, enhance antioxidant capacity, accelerate fatty acid β-oxidation, stimulate steroid hormone secretion, and provide sufficient energy for ovarian development in the giant freshwater prawn.

How does buffering-bridging alignment influence supply chain resilience? A polynomial regression analysis

Generic drug entry into the pharmaceutical market typically leads to a substantial decline in originator sales. Understanding the extent and trajectory of this erosion is essential for effective lifecycle management and strategic planning. This study quantified sales erosion after generic entry for originator drugs approved in the United States between 2010 and 2019 and developed a model to predict year-specific sales retention based on key product- and market-level characteristics. A total of 140 originator drugs were analyzed using FDA approval records and sales data from Evaluate Pharma. Five-year retention patterns were modeled using a three-parameter exponential decay function. Subgroup analyses were conducted by year of generic entry, therapeutic class, and product-specific features. A polynomial regression model using 700 product-year observations incorporated three binary market indicators and linear and quadratic time terms. Sales retention declined from 73.1% in the first year after generic entry to 31.7% by year five. The exponential decay model demonstrated a strong goodness-of-fit (root mean squared error [RMSE] = 0.006), capturing the initial steep decline and subsequent stabilization. Subgroup analyses showed faster erosion for blockbuster drugs and in markets with multiple first-generation generics. The regression model explained 96.4% of annual variation in retention (RMSE = 0.033), accounting for product and market heterogeneity. Sales decline after generic entry follows a predictable yet heterogeneous trajectory shaped by product and market factors. Exponential decay and polynomial regression models together offer a robust framework for forecasting sales retention and guiding strategic decisions in the pharmaceutical industry.

Efficient monitoring of lower-limb coordination is important for understanding movement characteristics during off-ice speed-skating training. This study aimed to develop an analytical framework to characterize the kinematic–kinetic coupling of the lower limbs during slideboard skating tasks using wearable sensors. Eight national-level junior speed skaters performed standardized simulated skating movements on a slideboard while wearing sixteen six-axis inertial measurement units (IMUs) and Pedar-X in-shoe plantar-pressure insoles. Joint-angle trajectories and plantar-pressure signals were temporally synchronized and preprocessed using a Kalman-based multimodal state-estimation approach. Third-order polynomial regression models were applied to examine the nonlinear relationships between hip–knee joint angles and plantar loading across four distinct movement phases. The results demonstrated consistent coupling patterns between angular displacement and peak plantar pressure across phases (R2 = 0.72–0.84, p < 0.01), indicating coordinated behavior between joint kinematics and plantar kinetics during simulated skating movements. These findings demonstrate the feasibility of a Kalman-based joint analysis framework for fine-grained assessment of lower-limb coordination in slideboard speed-skating training and provide a methodological basis for future investigations using wearable sensor systems.

A novel simplified structure model for accurate and flexible simulation of radiation-induced DNA damage.