Nonlinear Relationship Research Articles

3D polycatenated architected materials

Architected materials derive their properties from the geometric arrangement of their internal structural elements. Their designs rely on continuous networks of members to control the global mechanical behavior of the bulk. In this study, we introduce a class of materials that consist of discrete concatenated rings or cage particles interlocked in three-dimensional networks, forming polycatenated architected materials (PAMs). We propose a general design framework that translates arbitrary crystalline networks into particle concatenations and geometries. In response to small external loads, PAMs behave like non-Newtonian fluids, showing both shear-thinning and shear-thickening responses, which can be controlled by their catenation topologies. At larger strains, PAMs behave like lattices and foams, with a nonlinear stress-strain relation. At microscale, we demonstrate that PAMs can change their shapes in response to applied electrostatic charges. The distinctive properties of PAMs pave the path for developing stimuli-responsive materials, energy-absorbing systems, and morphing architectures.

Methods for Estimating the Exposure-Response Curve to Inform the New Safety Standards for Fine Particulate Matter

Abstract Exposure to fine particulate matter (PM2.5) poses significant health risks and accurately determining the shape of the relationship between PM2.5 and health outcomes has crucial policy implications. Although various statistical methods exist to estimate this exposure-response curve (ERC), few studies have compared their performance under plausible data-generating scenarios. This study compares seven commonly used ERC estimators across 72 exposure-response and confounding scenarios via simulation. Additionally, we apply these methods to estimate the ERC between long-term PM2.5 exposure and all-cause mortality using data from over 68 million Medicare beneficiaries in the United States. Our simulation indicates that regression methods not placed within a causal inference framework are unsuitable when anticipating heterogeneous exposure effects. Under the setting of a large sample size and unknown ERC functional form, we recommend utilizing causal inference methods that allow for nonlinear ERCs. In our data application, we observe a nonlinear relationship between annual average PM2.5 and all-cause mortality in the Medicare population, with a sharp increase in relative mortality at low PM2.5 concentrations. Our findings suggest that stricter limits on PM2.5 could avert numerous premature deaths. To facilitate the utilization of our results, we provide publicly available, reproducible code on Github for every step of the analysis.

Forecasting Agricultural Trade Based on TCN-LightGBM Models: A Data-Driven Decision

Facing the increasing complexity and dynamic fluctuations of the global agricultural trade market, accurate forecasting plays a key role in supporting agricultural policy formulation, stabilising the market and optimising resource allocation. In order to increase the precision and stability of agricultural trade predictions, this research suggests a hybrid model built on a temporal convolution network (TCN) and a lightweight gradient boosting tree (LightGBM). The TCN module effectively captures the long-term dependence characteristics of time series data through dilated convolution, which improves the model’s ability to identify seasonal and periodic trends. The LightGBM module, on the other hand, makes use of the characteristics of gradient boosting decision trees and excels at efficiently handling nonlinear relationships and avoiding overfitting. Experimental results show that the TCN-LightGBM model outperforms traditional models in terms of mean square error (MSE), mean absolute error (MAE) and prediction accuracy. Specifically, compared with ARIMA, LSTM, TCN alone or LightGBM alone, TCN-LightGBM achieves a prediction accuracy of 91.3% on the test data, with MSE and MAE of 0.021 and 0.115 respectively, significantly improving prediction accuracy and stability. In addition, parameter sensitivity analysis shows that the TCN-LightGBM model maintains a highly consistent prediction trend under different parameter configurations, which verifies the robustness of the model and its practical application value. This study provides a data-driven decision support tool with high accuracy and strong stability, providing a new solution for agricultural trade forecasting and other complex time series prediction tasks.

Examining the influence of port ship activities on pollutant emissions in port environments.

There is a direct and close relationship between ship emissions in port waters and the operational status of the ships. Precisely identifying the operational status of ships in port waters and thoroughly exploring the specific relationship between these activities and ship emissions is crucial for achieving accurate control and scientific reduction of emissions from ships in port areas. With advancements in technology, AIS data can accurately capture the operational status of ships, facilitating a macro-level analysis of ship behavior and emission characteristics. This study proposes a method for extracting ship activity states using AIS data and conducts a detailed examination of ship activities at various container terminals and berths within Shanghai Port. Additionally, it analyzes the correlation between ship activities and their emissions. The research findings indicate that container ships are the most prevalent ships at Shanghai Port, followed by bulk carriers, general cargo ships, and tankers. Notably, bulk carriers and tankers exhibit the longest berthing times, with tankers showing the most significant fluctuations. Mingdong Terminal is identified as the most active, featuring the longest anchorage and berthing time, whereas Jungonglu and Zhanghuabang Terminals have the shortest. The calculation of pollutant emissions reveals that container ships and oil tankers are the primary contributors, particularly for CO2 and NOx emissions. Mingdong Terminal recorded the highest total CO2 emissions, followed by Guandong and Shengdong Terminals. These findings emphasize the importance of berth service efficiency, suggesting that increased emissions are associated with heightened ship activity. CO2 emissions from container ships increase linearly with the number of berthed ships and show a cubic nonlinear relationship with berthing time. The analysis highlights terminals such as Guandong, Zhendong, Shengdong, and Yangshan Phase IV as critical areas for emission reduction strategies. This study not only enhances our understanding of the dynamics of ship emissions in port waters but also provides a theoretical foundation for implementing effective emission control and reduction strategies. Through this detailed research approach, it is possible to more accurately identify emission sources and optimize port operations, thereby offering strong data support and scientific guidance for environmental management and policy-making in port waters.

The health effect of relaxing entry regulation for private hospitals and its nonlinear characteristics: evidence from China

IntroductionRelaxing entry regulation for private hospitals and fostering competition in the healthcare market are crucial prerequisites for addressing the diverse healthcare demands of the population and promoting the development of a Healthy China. This study aims to comprehensively evaluate the health effect of relaxing entry regulation for private hospitals and to examine its nonlinear characteristics.MethodsUsing panel data from 31 provinces in mainland China, this study employs a fixed effects panel data model to investigate the health effect of relaxing entry regulation for private hospitals. To examine the potential nonlinear relationship, a panel threshold model is also employed. This study also employs a dynamic panel model as the econometric method to perform regression analysis for robustness testing.ResultsThe empirical findings indicate that relaxing entry regulation for private hospitals significantly improves the residents’ health level. This conclusion remains robust when different explanatory variables, measurement models and modified samples are applied. The heterogeneity analysis reveals that the health benefits of private hospital market entry are more pronounced in Central-Western region, regions with high medical resource endowment, and regions with High-quality competition. Furthermore, the health effect of relaxing entry regulation for private hospitals exhibits nonlinear characteristics: it weakens as economic development level reaches a certain threshold and becomes more pronounced as educational attainment reaches a specific threshold.DiscussionBased on these empirical results, Chinese provinces can be classified into three distinct types to guide the development of differentiated policies tailored to local conditions. This study provides valuable theoretical insights into promoting a fair competition mechanism in the healthcare market, enhancing the quality of private hospitals, and improving the overall health level of residents in China and other developing countries facing similar challenges.

The Application of Game Theory-Interesting Phenomena Between Time Pressure and Risk in Chess

This essay explores the application of game theory in chess, focusing on the relationship between time pressure, risk, and draw probability. Game theory provides a framework for analyzing interactive decision-making processes, enabling players to understand opponents' strategies, predict moves, and formulate optimal responses. The study utilizes a dataset of 20,058 chess games to examine the impact of duration on risk behavior. The analysis reveals a nonlinear relationship between game length and draw probability, with a parabolic trend suggesting that the likelihood of a draw increases with game length up to approximately 60-70 minutes, where it peaks at around 4%-5%, and then gradually decreases for longer games. The regression model shows time pressure leads to about 10% more risk-taking, indicating a moderate fit. These findings underscore the importance of time management and risk assessment in chess, with implications for enhancing players' competitive edge and strategic planning skills in both chess and real-world decision-making scenarios

Cardiometabolic Index and Stress Urinary Incontinence in US Women: The Mediating Role of the Triglyceride Glucose Index.

Stress urinary incontinence (SUI) is a prevalent condition among women, significantly impairing their quality of life. Emerging evidence suggests that metabolic dysfunction may play a role in the development of SUI, although the underlying mechanisms remain unclear. This study aims to examine the association between the cardiometabolic index (CMI), a novel marker of metabolic health, and the risk of SUI in women. Cross-sectional data from the 2001-2020 NHANES were analyzed. Weighted multivariable logistic regression models assessed the relationship between CMI and SUI risk, while restricted cubic spline (RCS) models examined potential nonlinear associations. Subgroup analyses and interaction tests were performed to explore how specific characteristics influenced the CMI-SUI relationship. Mediation analysis was performed to evaluate whether the triglyceride glucose (TyG) index mediated the CMI-SUI association. Sensitivity analyses using propensity score matching (PSM) ensured the robustness of the findings. Higher CMI was significantly associated with increased SUI risk in women (P < 0.001). RCS analysis revealed a nonlinear relationship, with a threshold at 1.64. Below this point, reducing CMI was significantly associated with a lower risk of SUI (overall P < 0.001, linear P < 0.001). Subgroup and interaction analyses showed stronger associations among women under 65years, those with higher education, those without a history of hypertension or diabetes, and women taking oral contraceptives (P for interaction < 0.05). Mediation analysis showed that the TyG index completely mediated the relationship between CMI and SUI, accounting for 97.67% of the total effect. Sensitivity analyses using PSM confirmed the robustness of these results. This study highlights that a higher CMI is associated with an increased risk of SUI in women, and this relationship may be largely mediated by the TyG index.

Optimizing Power Quality in EV Chargers Using Advanced Quadrature Signal Generators and AI‐Driven Adaptive Filtering

ABSTRACTAs electric vehicle (EV) adoption grows, vehicle‐to‐grid (V2G) technology enables bidirectional power flow in grid‐interactive EV chargers. However, maintaining consistent power quality under nonideal grid conditions remains a challenge. Traditional PI controllers struggle to reduce total harmonic distortion (THD) and adjust to dynamic grid variations. This study explores machine learning techniques, including decision trees, artificial neural networks (ANN), and linear regression, as alternatives to conventional PI controllers. Decision trees emerge as the most advantageous due to their simplicity, interpretability, and ability to handle complex, nonlinear relationships with minimal data preprocessing. While ANN captures intricate patterns, it demands more computational resources and lacks transparency. Linear regression, though efficient, struggles with complex grid behaviors. The decision tree approach allows real‐time adaptive control, improving THD reduction and grid stability. Additionally, a CNISOGI filter is implemented to enhance harmonic attenuation and DC‐offset rejection. The system's effectiveness is validated through Matlab/Simulink simulations and a 1.1 kW hardware prototype. The results show that integrating decision tree‐based controllers with advanced filtering techniques can significantly enhance power quality, grid stability, and operational efficiency in future smart grids.

The association between working hours and working type with non-alcoholic fatty liver disease: results from the NHANES 1999-2014

BackgroundPrevious research has indicated that long working hours are connected to a variety of health conditions, including nonalcoholic fatty liver disease (NAFLD). However, this association which has been observed in more population is limited. Our research is designed to evaluate the association between working hours, working type, and NAFLD.MethodsThe study comprised adults with complete details on working hours, working type, and NAFLD from the NHANES 1999-2014. We employed the hepatic steatosis index (HSI) to evaluate NAFLD and examined the relationship between working hours or working type and hepatic steatosis using weighted multiple-variable regression models and restricted cubic spline (RCS) analysis. In addition, further subgroup analysis was performed based on sex, age, ratio of family income to poverty (PIR), education, and diabetes.ResultsLong working hours were significantly linked to an elevated risk of NAFLD (OR: 1.57, 95%CI: 1.21-2.05), even after controlling for confounding factors. RCS analysis suggested that there was no nonlinear relationship between them. When weekly working hours &amp;gt; 50, the likelihood of NAFLD among the population heightened to 57% and this risk increased to 99% in the female population. As for working type, increasing physical intensity of work was associated with higher NAFLD risk, but only heavy manual labor continued to show significance after adjustment (OR:1.39, 95%CI: 1.06-1.81). We observed that the relationship between heavy manual labor and NAFLD was more significant in the older and male populations.ConclusionOur results indicate that long working hours and engaging in heavy physical labor are independent risk factors for NAFLD. As working hours increase and individuals engage in heavy physical labor for extended periods, the risk of developing NAFLD significantly rises.

Association of pan-immune inflammation value and lung health in adults

BackgroundLung health is intricately linked with inflammation. The pan-immune-inflammation value (PIV) emerges as a promising biomarker, offering reflection into systemic inflammatory states and assisting in the prognosis of diverse diseases. This research aims to explore the associations between PIV and respiratory symptoms, respiratory diseases and lung function.MethodsThe study was a cross-sectional population study from the National Health and Nutrition Examination Survey (NHANES). Restricted cubic spline (RCS) models were conducted to explore the relationships between PIV and respiratory health outcomes, while weighted linear regression models and weighted logistic regression models were the ones used for regression analysis. Trend tests probed the evolving relationship among PIV quartiles and outcomes. The study incorporated subgroup analysis and interaction tests to examine associations within specific subpopulations.ResultsFrom the cohort of 6,263 participants, a distinct negative correlation was identified between PIV and lung health. Subsequent to confounding factors, a 100-unit increment in PIV was linked to a 2% increase in the incidence of cough and phlegm (OR, 95% CI: 1.02, 1.00 to 1.05; 1.02, 1.00 to 1.04). Additionally, higher PIV was associated with reductions in FEV1 (MD, 95% CI: -5.37, -9.10 to -1.64) and FVC (MD, 95% CI: -5.75, -10.34 to -1.15). Categorizing PIV into quartiles revealed an ascending trend: A significantly higher risk of cough/phlegm/wheeze was found in participants in the second/third/fourth PIV quartile compared to those in the first PIV quartile (all p for trend < 0.05). Moreover, lung function indicators (FEV1, FEV1%, FVC, FVC%, FEV1/FVC) declined significantly in the fourth quartile (all p for trend < 0.05). Besides, a nonlinear relationship between PIV and outcomes was evident. Subgroup analysis revealed variations in these associations stratified by gender, age, smoking and drinking status, as well as certain disease history.ConclusionsThe study highlighted the potential connections between PIV and respiratory symptoms, respiratory diseases and lung function. Monitoring PIV level could provide valuable insights into the inflammatory status and may inform clinical approaches for managing respiratory health.

Lateral End-Range Movement Profile and Shot Effectiveness During Grand Slam Tennis Match-Play.

End-range movements are among the most demanding but least understood in the sport of tennis. Using male Hawk-Eye data from match-play during the 2021-2023 Australian Open tournaments, we evaluated the speed, deceleration, acceleration, and shot quality characteristics of these types of movement in men's Grand Slam tennis. Lateral end-range movements that incorporated a change of direction (CoD) were identified for analysis using k-means (end-range) and random forest (CoD) machine learning models. Peak speed, average deceleration into the CoD, average reacceleration out of the CoD, and the quality of the shot played were computed. Players were grouped based on their ATP rankings (top 10, top 50, and outside top 50) to examine the influence of ranking on movement profiles and shot effectiveness. Our data showed that end-range movements profiles of top 10 and top 50 players were characterized by higher peak speed (d=0.3-0.88), deceleration intensity (d=0.25-0.63), and acceleration intensity (d=0.06-0.51) when compared to players outside the top 50 (p<0.05). Top 10 players also demonstrated greater peak speeds (d=0.59) and acceleration intensities (d=0.45) compared to top 50 players (p<0.05). There was a nonlinear inverse relationship between peak speed and shot quality, such that, as peak speed increased, shot quality decreased-notwithstanding that top 10 players were more likely to hit high-quality shots at higher peak speeds. These results quantify the discrete kinematic characteristics of the sport's most challenging movement sequence and reveal, for the first time, that higher ranked players may possess superior movement potential on court.

An Integrated Stacking Ensemble Model for Natural Gas Purchase Prediction Incorporating Multiple Features

Accurate prediction of natural gas purchase volumes is crucial for both the economy and the environment. It not only facilitates the rational allocation of resources for companies but also helps to reduce operational costs. Although existing prediction methods have achieved some success in addressing the nonlinear relationships in natural gas purchases, there remains potential for further improvement. To address this issue, a stacking ensemble learning model was developed to enhance the ability to handle complex nonlinear problems. This model integrates diverse algorithms and incorporates weather factors, while regionalizing characteristics of natural gas usage, thereby achieving accurate forecasts of natural gas purchase volumes. We selected three distinctly different base models—Informer, multiple linear regression (MLR), and support vector regression (SVR)—for our research. By conducting four different feature combination experiments for each base model, including weather, time, regional, and usage features, we constructed 12 foundational models. Subsequently, we integrated these base models using a meta-learner to form the final stacking ensemble model. The experimental results indicate that the stacking ensemble model outperforms individual models across key metrics, including R2, MRE, and RMSE. Notably, the R2 values improved by 4–15% compared to the 12 base models. The model was subsequently applied to predict natural gas purchase volumes in Pi County, Chengdu, China. In November 2024, a side-by-side comparison of the predicted and actual data revealed a maximum error of just 5.39%. This exceptional accuracy effectively meets forecasting requirements, underscoring the model’s predictive strength in the energy sector.

The prognostic value of the platelet-to-lymphocyte ratio in multiple myeloma patients treated with a bortezomib-based regimen

Multiple myeloma (MM) is the second most common hematological malignancy. Previous studies have validated the prognostic significance of the platelet-to-lymphocyte ratio (PLR) in patients with certain solid tumors. However, the relationship between the PLR and prognosis in myeloma patients has not been clearly demonstrated. In our study, we included 122 newly diagnosed MM patients who were treated with bortezomib-based chemotherapy. These patients were divided into low-PLR and high-PLR groups based on their initial PLR values. We compared the clinical characteristics between the two groups and utilized restricted cubic splines (RCSs) in the regression model to estimate the nonlinear relationship between the initial PLR and overall survival (OS) in MM patients. The results showed that patients in the low-PLR group had significantly worse OS (P = 0.00031) and progression-free survival (PFS) (P < 0.0001) compared to those in the high-PLR group. Furthermore, within the higher-risk MM group, a low PLR was also associated with worse OS (P = 0.0037) and PFS (P = 0.0048). Therefore, a low PLR was identified as an independent predictor of poor OS in MM patients. The RCS curves further confirmed a significant nonlinear relationship between the PLR and OS in patients with MM. The PLR may serve as a significant independent prognostic indicator for MM patients undergoing bortezomib-based chemotherapy, and there exists a crucial nonlinear relationship between the PLR and OS in these patients.

Unleashing the green potential: exploring the dynamic influence of the urban digital economy on carbon emissions

In the backdrop of “dual-carbon” strategic objectives, understanding the influence of the digital economy (DE) on carbon emissions (CEs) is imperative. However, there is limited research on the DE’s negative impact on CEs and the nonlinear relationship between the DE and CE. To address this gap, we collected data from 270 Chinese cities from 2011 to 2021 and used benchmark regression, mediated effects, and panel threshold models to explore the DE’s impact on CEs. The results showed that DE had a nonlinear, inverted U-shaped effect on CEs, with CEs initially increasing and then being suppressed. This conclusion remained consistent even after a series of robustness tests. Overall, the rate of urbanization and breadth of digital financial coverage mediate the relationship between the DE and CEs. Additionally, the combined effects of economic development, environmental regulation, fiscal decentralization, and population size contribute to the DE’s nonlinear impact on CEs. The impact of the DE on CEs varies among nonresource-based, resource-based, and resource-depleted cities and between urban and nonurban agglomerations. This paper’s findings support the development of the DE and the formulation of CE reduction policies.

Multiscale Nonlinear Response of Extreme Meteorological–Hydrothermal Events in the Upper Reaches of the Yangtze River

ABSTRACTUnder the backdrop of climate warming, the outbreak of short‐term extreme heat events can easily lead to irreversible changes in aquatic ecosystems. Delving into their intrinsic driving mechanisms and nonlinear characteristics is key to preventing natural disasters. This study, focusing on the upper Yangtze River as the research area, constructs a joint copula function model to analyze the joint occurrence probability and return period of extreme meteorological heat events. Through the bivariate cross–wavelet transform method, the study explores the multiscale dynamic response relationships and phase characteristics of extreme meteorological–hydrothermal events in the upper Yangtze River. Furthermore, a joint multifractal model of nonlinear responses for extreme meteorological–hydrothermal events was established. The results indicate that extreme high‐heat meteorological events in the upper Yangtze River tend to occur more frequently and severely, with duration–kurtosis events likely to coincide within a 2‐year return period, as well as high‐intensity low‐frequency high‐heat duration–severity events occurring simultaneously. Overall, before 2005, extreme high‐hydrothermal events exhibited phase characteristics lagging behind meteorological changes, which then shifted from lag to lead. Under three scenarios of change, meteorological–hydrothermal events exhibit a clear nonlinear response relationship. Apart from duration, severity and kurtosis all show significant nonlinear relationships.

Analysis of mechanical properties and energy evolution mechanism of frozen calcareous clay under multi-factor interaction

Research investigating the complex mechanical properties and energy evolution mechanisms of frozen calcareous clay under the influence of multiple factors is crucial for optimizing the artificial ground freezing method in shaft sinking, thereby enhancing construction quality and safety. In this study, a four-factor, four-level orthogonal test was devised, taking into account temperature, confining pressure, dry density, and water content. The complex nonlinear curvilinear relationship between deviatoric stress, volume strain, and axial strain of frozen calcareous clay under different interaction levels was analyzed. The sensitivity of each factor to the peak volume strain was explored, and the energy evolution mechanism of frozen calcareous clay during the triaxial compression process was analyzed. The findings are summarized as follows: (1) The deviatoric stress-axial strain curves demonstrate the strain-hardening characteristics of frozen calcareous clay specimens. Furthermore, as temperature decreases, the hardening degree increases. (2) Sensitivity analysis indicates that the factors’ influence on peak volumetric strain ranks as follows: dry density > confining pressure > temperature > water content. Under the various interactions, specimens exhibit significant volumetric shrinkage. When the temperature remains constant, peak volumetric strain is negatively correlated with dry density but positively correlated with confining pressure. (3) Input energy density, elastic strain energy density, and dissipated energy density of frozen calcareous clay all increase with axial strain. (4) When temperature is held constant, both peak input energy density and peak dissipated energy density rise with increasing confining pressure. Meanwhile, peak elastic strain energy density shows a linear increase with higher confining pressure and lower temperatures.

The Impact of Farmland Transfer on Urban–Rural Integration: Causal Inference Based on Double Machine Learning

Urban–rural fragmentation represents a significant challenge encountered by nations globally, particularly in both developing and developed contexts, during the modernisation process. This study examines the effects of rural land system reform on facilitating integrated development between urban and rural areas. The analysis of the impact of the 2010 liberalisation of the land transfer policy employs a dual machine learning model, utilising provincial-level data from China spanning 2005 to 2022, to address the limitations of traditional causal inference models while ensuring estimation accuracy. The findings indicate that the reform of the rural land system significantly enhances integrated urban–rural development, particularly in demographic, economic, and ecological dimensions. The mechanisms encompass the facilitation of extensive land and agricultural service operations, the development of new business entities, the migration of rural labour, and the enhancement of agricultural capital. Furthermore, notable disparities exist in the effects of reforms across various regions, particularly concerning urban–rural integration development and land transfer levels. The policy effects of land transfer exhibit a marginally diminishing trend. The influence of land transfer on urban–rural integration varies with economic development levels, demonstrating a nonlinear relationship, with the most pronounced effects observed in regions with moderate economic development. Additionally, the policy effects of land transfer differ based on geographic location. The impact of land transfer policies varies across geographic regions, with the central region exhibiting the most significant effect, followed by the north-eastern region, the western region, and the eastern region, which shows the least effect. This study provides a reference for advancing the reform of the marketisation of land factors, improving the efficiency of land resource allocation, and regionally and in multiple layers advancing the reform of the rural land system.

Analysis of nonlinear behavior of viscoelastic damping in musical membranes using physics-informed self-organizing maps

This research offers a new analytical tool that unravels the nonlinear relation between the parameters of Viscoelastic Damping (VD) and the resulting frequency spectrum in musical membranes. Understanding how variations in VD parameters influence the resulting sounds is crucial for developing new tools for artistic expression and for designing musical instruments with distinct sound qualities. In the case of membranophones, the external damping is well understood, while the internal damping due to viscoelastic properties of materials remains unclear. In previous research, VD in musical membranes has been modeled using a Finite-Difference Time-Domain (FDTD) model. Nonetheless, analyzing the complex relationships between the large parameter space of the model and the nonlinear behavior of VD is a challenging task. This study addresses this analysis through physics-based machine learning. We employed a FDTD model of a viscoelastically damped membrane to create a physics-informed dataset, which we subsequently analyzed using Self-Organizing Maps (SOMs). Our findings reveal that the damping coefficient is the primary criterion when clustering the data. Furthermore, we found the internal structure of the cluster to depend on the rate of decay of the memory effect, i.e., the rate at which the energy introduced back into the system decreases. The study also demonstrates the benefits of using principal component analysis for the SOM initialization.

High‐Frequency Instruments and Identification‐Robust Inference for Stochastic Volatility Models

ABSTRACTWe introduce a novel class of stochastic volatility models, which can utilize and relate many high‐frequency realized volatility (RV) measures to latent volatility. Instrumental variable methods provide a unified framework for estimation and testing. We study parameter inference problems in the proposed framework with nonstationary stochastic volatility and exogenous predictors in the latent volatility process. Identification‐robust methods are developed for a joint hypothesis involving the volatility persistence parameter and the autocorrelation parameter of the composite error (or the noise ratio). For inference about the volatility persistence parameter, projection techniques are applied. The proposed tests include Anderson‐Rubin‐type tests and their point‐optimal versions. For distributional theory, we provide finite‐sample tests and confidence sets for Gaussian errors, establish exact Monte Carlo test procedures for non‐Gaussian errors (possibly heavy‐tailed), and show asymptotic validity under weaker assumptions. Simulation results show that the proposed tests outperform the asymptotic test regarding size and exhibit excellent power in empirically realistic settings. The proposed inference methods are applied to IBM's price and option data (2009–2013). We consider 175 different instruments (IVs) spanning 22 classes and analyze their ability to describe the low‐frequency volatility. IVs are compared based on the average length of the proposed identification‐robust confidence intervals. The superior instrument set mostly comprises 5‐min HF realized measures, and these IVs produce confidence sets which show that the volatility process is nearly unit‐root. In addition, we find RVs with higher frequency yield wider confidence intervals than RVs with slightly lower frequency, indicating that these confidence intervals adjust to absorb market microstructure noise. Furthermore, when we consider irrelevant or weak IVs (jumps and signed jumps), the proposed tests produce unbounded confidence intervals. We also find that both RV and BV measures produce almost identical confidence intervals across all 14 subclasses, confirming that our methodology is robust in the presence of jumps. Finally, although jumps contain little information regarding the low‐frequency volatility, we find evidence that there may be a nonlinear relationship between jumps and low‐frequency volatility.

The Multivariate Fusion Distribution Characteristics in Physician Demand Prediction

Aiming at the optimization of the big data infrastructure in China’s healthcare system, this study proposes a lightweight time series physician demand prediction model, which is especially suitable for the field of telemedicine. The model incorporates multi-head attention mechanisms and generates statistical information, which significantly improves the ability to process nonlinear data, adapt to different data sources, improve the computational efficiency, and process high-dimensional features. By combining variational autoencoders and LSTM units, the model can effectively capture complex nonlinear relationships and long-term dependencies, and the multi-head attention mechanism overcomes the limitations of traditional algorithms. This lightweight architecture design not only improves the computational efficiency but also enhances the stability in high-dimensional data processing and reduces feature redundancy by combining the normalization process with statistics. The experimental results show that the model has wide applicability and excellent performance in a telemedicine consulting service system.