Kernel Density Research Articles

Efficient prediction uncertainty quantification in dam behavior monitoring with attention-based sequence-to-sequence learning

Displacement is an intuitive monitoring indicator of dam structural behavior. Conventional deterministic modeling methods frequently disregard the inherent uncertainty associated with monitoring data. This study aims to quantify such uncertainties within dam displacement predictions by augmenting a sequence-to-sequence structure with the novel recurrent unit, termed as tiny gated unit (TGU), attention mechanism, as well as quantile regression, resulting in the Att-S2STQ model. Specifically, TGU adopts only one gate to identify nonlinearity in data sequences, while Bahdanau attention mechanism dynamically assigns weights to different parts of the input sequence. The inclusion of quantile regression allows Att-S2STQ to produce prediction intervals (PIs), from which the probability density functions (PDFs) and cumulative distribution functions (CDFs) are further derived via kernel density estimation. PIs, PDFs, and CDFs jointly serve to reveal the prediction uncertainty. The effectiveness of the model is illustrated through comparative experiments using real-world dam monitoring datasets. Results indicate that the proposed model outperforms traditional methods in point, interval, and probability predictions, while also having a simpler structure and faster training. The superiority of both accuracy and efficiency makes it a valuable tool for dam management, aiding in data-driven decision-making and enhancing operational safety.

From Imbalance to Synergy: The Coupling Coordination of Digital Inclusive Finance and Urban Ecological Resilience in the Yangtze River Economic Belt

In the context of rapid urbanization and digitalization, scientifically assessing the spatio-temporal interaction between digital inclusive finance (DIF) and urban ecological resilience (UER) is crucial for promoting the coordinated development of the regional ecology and economy. This study investigates the spatiotemporal evolution of the coupled coordination degree (CCD), the decoupling phenomenon, and its hindering factors in the Yangtze River Economic Belt (YREB) by utilizing the kernel density analysis, standard deviation ellipse, decoupling model, and obstacle degree analysis. Through systematic analyses, this paper aims to elucidate the development disparities among regions within the YREB, identify problematic areas, and propose targeted improvement measures. The results show that (1) The CCD between DIF and UER in the YREB has increased annually from 2011 to 2020. However, there are persistent imbalances, with an overall low level of coordination and uneven spatial development, and a trend of “higher coordination in the east and lower coordination in the west”. (2) The overall CCD of the YREB has reached at least the primary coordination level, with the coupling enhancement speed ranked as “downstream > midstream > upstream”, and regional differences decreasing. (3) The decoupling analysis reveals a predominant decoupling trend between DIF and UER, indicating that the digitization of financial services has not concurrently increased ecological pressures. (4) The obstacle degree analysis identifies resilience and digitalization as major barriers hindering CCD. This study provides a scientific basis and analytical framework for understanding the current spatiotemporal interaction between DIF and UER in the YREB, offering an important reference for formulating more effective policies.

Research on the Spatial–Temporal Distribution and Morphological Characteristics of Ancient Settlements in the Sichuan Basin

An investigation into the spatial–temporal distribution characteristics of ancient settlements and their relationship with the environment in the Sichuan Basin can enhance our understanding of the evolution of the regional human–land relationship. Utilizing kernel density analysis by GIS, this paper obtained the spatial distribution characteristics of 1100 settlements in the Neolithic, Shang–Zhou, and Qin to Southern Dynasties periods. Subsequently, a GIS spatial analysis was performed to examine the distribution of these settlements in relation to the natural environment, focusing on four aspects: elevation, slope, aspect, and water buffer zone. The results demonstrate that: (1) The distribution of settlements from the Neolithic to the Southern Dynasties has expanded from the Chengdu Plain in the west and the Xiajiang Area in the east to the hilly areas in the center. (2) The settlements in the Neolithic and Shang–Zhou periods are predominantly located at elevations between 300–600 m, slopes between 0–3°, aspects between 135–225°, distances to rivers between 0–1000 m, and soil choice on Luvisols, Cambisols, Regosols, and Anthrosols. The influence of aspect on settlements during the Qin–Southern Dynasties period was notably reduced. The settlements mainly grow in the Chengdu Plain and the smaller plains along the river from the Neolithic to the Southern Dynasties in the Sichuan Basin. (3) The emergence and advancement of primitive agriculture, the construction of early water conservancy facilities, commercial and trade exchanges, and the establishment of regimes led to a shift from a double core to a more dispersed distribution in the Sichuan Basin from the Neolithic to the Southern Dynasties periods. The evolution of settlements reflects the adaption and competition of the residents to the natural environment in the Sichuan Basin. Furthermore, it provides insights into the complex social development in the region, ranging from the formation of early states to the establishment of the Qin and Han Empires.

Spatiotemporal evolution and driving factors of the coupling coordination of the population‒land‒water‒industry system in the lower Yellow River

Exploring the interaction and coupling effects within the population‒land‒water‒industry (PLWI) system is conducive to promoting high-quality regional sustainable development. Taking the lower Yellow River during the period from 2000 to 2020 as a research sample, this study used the entropy weight TOPSIS method, the coupling coordination degree (CCD) model and kernel density estimation to synthetically evaluate the CCD of the PLWI system. The GeoDetector model was applied to explore the factors influencing the CCD of the PLWI system considering the nonlinear relationship. The major results can be summarized as follows: (1) From 2000 to 2020, the comprehensive development index (CDI) of the population, land, water and industry subsystems followed a gradual upward trend in the lower Yellow River, increasing by 0.293, 0.033, 0.111 and 0.369, respectively. However, the CDI of the land subsystem varied greatly between regions. Some cities, such as Jinan, Jining and Binzhou, experienced large declines in the CDI of the land subsystem, from 0.433, 0.534 and 0.572 to 0.358, 0.481 and 0.522, respectively. (2) The CCD of the PLWI system in the lower Yellow River showed an upward trend, increasing from 0.481 to 0.678, and became more concentrated during 2000–2020. Most of the region transitioned from near disorder to primary coordination. (3) Factors such as number of health technicians per 10,000 people, average salary, number of college students per 10,000 people, per capita GDP and per capita education expenditure were critical to the coordinated development of the PLWI system, the explanatory powers were 0.644, 0.639, 0.610, 0.498 and 0.455, respectively. Finally, this study proposed three policy recommendations to improve coupling coordination in the lower Yellow River Basin: Improving population quality, promoting green technology and rational land planning.

A category incremental continuous learning model for imbalance arrhythmia detection

Abstract The development of efficient arrhythmia detection systems is crucial for physiological measurements and computer-aided diagnosis. Existing systems rely mainly on offline learning methods and lack the ability to assimilate new data or recognize emerging categories. To address these challenges, this study introduces an arrhythmia detection model that is resistant to data imbalance and has continuous learning capabilities, specifically for incremental learning of new ECG data categories. The system incorporates constraints derived from the new class data and implements a dynamic mechanism for updating connection weights, facilitating the incremental continual learning of classes. Confronted with the problem of models forgetting the original data and overfitting with the added data in continuous learning, we introduce a data balancing method by regularization to balance the model's memory and learning of the two types of data. Facing the data imbalance problem in continuous learning, we introduce a posteriori probability weighting strategy. This strategy assigns greater importance to high-value samples based on the model's posterior residual kernel density estimates. Comprehensive testing of the model using various datasets from the MIT-BIH database indicates superior performance in incremental learning tasks. The results reveal that the model not only excels in class incremental learning but also ensures effective balancing across different data classes.

Dynamics of Feline Sporotrichosis in Espírito Santo, Brazil: Impact of Urbanisation.

Sporotrichosis is a chronic infectious mycosis caused by traumatic implantation of Sporothrix spp., which poses a significant challenge to public health because of its zoonotic nature. It affects humans and other animals, particularly cats. This study investigated epidemiological trends and spatial distribution of feline sporotrichosis in Espírito Santo between 2017 and 2022. This study collected diagnostic data on sporotrichosis from the Veterinary Pathology Laboratory and Center for Infectious Diseases in Espírito Santo from 2017 to 2022. Statistical analyses were performed using STATA and spatial analyses were performed using ArcGIS software to create maps and identify hotspots. Kernel density estimation and directional mean statistics were applied to visualise the disease concentration and transmission trends. The results showed a significant increase in feline sporotrichosis cases in Espírito Santo from 2017 to 2022, with hotspots identified in urban and densely populated areas. Anchieta, Aracruz and Vila Velha reported the highest numbers of cases. Spatial analysis indicated a spread towards the central and northern coastal regions. This study highlights the growing threat of feline sporotrichosis in Espírito Santo, Brazil, particularly in densely populated urban areas. This underscores the urgent need for comprehensive public health strategies that address urbanisation, human-animal interactions and managing stray cat populations. Effective control measures and enhanced surveillance are crucial to mitigate the spread of this zoonotic disease. Importantly, this study provides valuable insights into the epidemiology of sporotrichosis in Brazil and offers a framework for other regions identified as emerging hotspots that face similar challenges.

Experimental study on mechanical and acoustic emission characteristics of red sandstone containing combined flaws of hole-fissure under biaxial compression

To investigate the mechanical behaviour and failure mechanism of flawed rock masses under biaxial stress conditions, a series of biaxial compression experiments are conducted on red sandstone specimens containing combined flaws of the circular hole and perforated symmetric fissure combined with acoustic emission (AE) technology in this work. The results show a close association between the stress-strain curve morphology and confining stress, both the biaxial compression strength and elastic modulus exhibit an upward trend with increasing fissure angle and confining stress. The maximum AE energy and cumulative AE energy both increase with higher confining stress. The crack types in the specimens are identified by analyzing the AF/RA value distribution, revealing a gradual decrease in the percentage of tensile cracks with increasing fissure angle. An AE localization algorithm based on the least absolute value method is applied to pinpoint AE events during biaxial compression, and AE events distribution is analyzed through the Kernel density estimation (KDE). The crack extension behaviour is described based on the movement of the maximum kernel density points, which initially exhibits a progression from both ends of the specimen towards the central region and subsequently from the central fissure tip towards the two ends.

Spatiotemporal variations of farmland crop residue burning in China from 2013 to 2022

Farmland crop residue burning (FCRB) significantly impacts air quality, necessitating understanding its spatiotemporal variations to evaluate control measures and guide future policies. This study analyzes FCRB across China from 2013 to 2022 using remote sensing technology and spatiotemporal analysis. Results indicate that the first phase (2013–2017) of the “Clean Air Action” control measures has been proven ineffective, with a 30.9 % increase in FCRB. Effective measures implemented in the second phase (2018–2020) resulted in a reduction of 41.4 % and led to a decrease of 34.3 % in 2022 compared to 2013. FCRB exhibits significant seasonal and regional variations, with a 69 % decrease in autumn and a 23 % increase in spring. While the variations in FCRB across regions are found to be significantly negatively correlated with the stringency of control measures, there is a 61.2 % reduction in the central region, 42.4 % in the western region, 29.7 % in the eastern region with the highest intra-regional disparities, and only 4.5 % in the northeastern region, which is attributed to the high FCRB in Heilongjiang province. FCRB demonstrates the “club convergence” phenomenon and the spillover effects of adjacent provinces, leading to high-high clusters in the northeastern region, emphasizing the need for region-specific control measures (e.g., Heilongjiang province in the northeastern) and the implementation of similar control measures in adjacent areas. Additionally, it is necessary to avoid the rebound phenomenon determined by the analysis of the kernel density estimation curve. Our findings underscore the importance of tailored strategies in managing FCRB and improving air quality in critical areas.

Estimation of vessel link-level travel time distribution: A directed network-driven approach

Accurate vessel travel time estimation is essential for operational efficiency and route optimization. Despite the prevalent use of the automatic identification system (AIS) in garnering multifaceted real-time data, ambiguities and inaccuracies in travel time predictions persist. It leads to planning uncertainties, inefficient resource allocations, and heightened operational costs in maritime logistics. To addresses these issues, this paper proposed a nuanced method to enhance the precision and reliability of vessel travel time estimations. Firstly, a directed maritime network is constructed by extracting essential information from AIS-based historical vessel trajectories. This lays the foundation for the subsequent analytical processes. Secondly, the non-parametric kernel density estimation (KDE) is applied to this constructed network, enabling the estimation of vessel travel time distributions across various network links. The non-parametric KDE is used in combination with AIS data, which improves the specificity and accuracy of the travel time estimations at the link level. Finally, this paper employs cellular automata (CA) simulations to validate the accuracy of the KDE-based estimations. Comparison between the simulation results and real-world data reveals a high degree of accuracy in the proposed method, confirming its applicability and effectiveness in estimating vessel travel times.

An interval uncertainty modeling method based on information granulation and improved multidimensional parallelepiped

Interval uncertainty modeling is essential for non-probabilistic reliability analysis of uncertain structures in the context of small samples, which confronts the difficulties of obtaining marginal intervals and characterizing variables correlation. A novel method for interval uncertainty modeling based on information granulation and improved multidimensional parallelepiped is proposed in this paper. Firstly, the method for constructing marginal intervals of uncertain variables is presented by integrating the up-sampling method based on kernel density estimation and information granulation theory (KDE-IG). Secondly, a relatively simple correlation coefficient expression based on the correlation angle is defined, and an improved multidimensional parallelepiped modeling method is proposed by optimizing the correlation coefficient within the marginal intervals. Additionally, two evaluation indexes are proposed to evaluate the robustness and accuracy of the constructed model. Finally, the applicability and effectiveness of the proposed method are demonstrated through two examples.

Kernel density estimation of egg attachment areas aids in revealing spatiotemporal changes in Chinese sturgeon spawning grounds

Identifying precise egg attachment areas and tracking trends of spawning magnitude (total amount of spawned eggs) are critical for accurate habitat assessment and effective conservation efforts, especially for lithophilic spawning fishes. However, accurate measurement of spawning conditions across both spatial and temporal dimensions poses significant challenges. We conducted a fourteen-year field study below the Gezhouba Dam, the main spawning ground for the Chinese sturgeon, using Kernel Density Estimation (KDE) method and Catch per Unit of Effort (CPUE) to refine knowledge on egg attachment areas relative to previous assessments. In addition, our analysis documented shifts in spawning locations within these four areas over the past fourteen years, revealing a worrying trend of decreasing spawning magnitude. This approach not only enabled the incorporation of the density distribution of eggs into the assessment of spawning magnitude trends, but also underscored the potential of the KDE as a framework for identifying egg attachment areas and estimating spawning magnitude trends. Our results provide valuable insights into spawning degradation of Chinese sturgeon and inform conservation strategies to protect their fragile spawning grounds.

Confidence-based design optimization using multivariate kernel density estimation under insufficient input data

The uncertainty quantification of the input statistical model in reliability-based design optimization (RBDO) has been widely investigated for accurate reliability analysis, and it could be estimated through its characteristics, cumulative experiences, and available data. However, uncertainty quantification of random variables in existing RBDO studies has exploited parametric distributions quantifying the uncertainty through the Bayes' theorem. In addition, a correlation between random variables is often underestimated due to a lack of knowledge and difficulty to describe the high-dimensional correlation. Hence, it has been a challenge to properly quantify input statistical model and its uncertainty. Therefore, a multivariate kernel density estimation (KDE) is employed to perform data-driven confidence-based design optimization (CBDO) for effective quantification of input model uncertainty. Any assumption on input distribution is not necessary since it is established only with the given input data. Moreover, the input model uncertainty due to insufficient data is quantified using bootstrapping and optimal adaptive bandwidth matrices through the Bayes’ theorem using cross-validation error. Consequently, the proposed CBDO with given input data is capable of finding a conservative optimum of RBDO accounting for both aleatory uncertainty of random variables and epistemic uncertainty induced by a limited number of input data through the multivariate KDE.

Spin states of X-complex asteroids in the inner main belt

Context. Based on the V-shape search method, two families, Athor and Zita, have been identified within the X-complex population of asteroids located in the inner main belt. The Athor family is ~3 Gyr old while the Zita family could be as old as the Solar System. Both families were found to be capable of delivering near-Earth asteroids (NEAs). Moreover, the Athor family was linked to the low-iron enstatite (EL) meteorites. Aims. The aim of our study is to characterise the spin states of the members of the Athor and Zita collisional families and test whether these members have a spin distribution consistent with a common origin from the break up of their respective family parent asteroids. Methods. To perform this test, our method is based on the well-established asteroid family evolution, which indicates that there should be a statistical predominance of retrograde-rotating asteroids on the inward side of family’s V-shape, and prograde-rotating asteroids on the outward side of family’s V-shape. To implement the method, we used photometric data from our campaign and the literature in order to reveal the spin states, and hence their rotation sense (prograde or retrograde), of the asteroids belonging to these families. We combined dense and sparse-in-time photometric data in order to construct asteroid rotational light curves; we performed the light curve inversion method to estimate the sidereal period and 3D convex shape along with the spin axis orientation in space of several family member asteroids. Results. We obtained 34 new asteroid models for Athor family members and 17 for Zita family members. Along with the literature and revised models, the Athor family contains 60% (72% considering only the family’s core) of retrograde asteroids on the inward side and, conversely, 76% (77% considering only the family’s core) of prograde asteroids on the outward side. We also found that the Zita family exhibits 80% of retrograde asteroids on the inward side. In addition, the Zita family presents an equal amount of prograde and retrograde rotators (50% each) on the outward side. However, when we applied Kernel density estimation (KDE), we also found a clear peak for prograde asteroids on the outward side, as expected from the theory. Conclusions. The spin states of these asteroids validate the existence of both families, with the Athor family exhibiting a stronger signature for the presence of retrograde-rotating and prograde-rotating asteroids on the inner and outer side of the family, respectively. Our work provides an independent confirmation and characterisation of these very old families, whose presence and characteristics offer constraints for theories and models of the Solar System’s evolution.

Convergence Analysis of Mean Shift.

The mean shift (MS) algorithm seeks a mode of the kernel density estimate (KDE). This study presents a convergence guarantee of the mode estimate sequence generated by the MS algorithm and an evaluation of the convergence rate, under fairly mild conditions, with the help of the argument concerning the Łojasiewicz inequality. Our findings extend existing ones covering analytic kernels and the Epanechnikov kernel. Those are significant in that they cover the biweight kernel, which is optimal among non-negative kernels in terms of the asymptotic statistical efficiency for the KDE-based mode estimation.

Urban eco-efficiency of China: Spatial evolution, network characteristics, and influencing factors

Urban eco-efficiency (EE) refers to the ability of a city to balance economic growth with environmental protection through the optimal use of resources and environmental management, reflecting the city’s performance in sustainable development. Quantitative EE analysis is a crucial evaluation criterion for measuring the process of sustainable development (SD). To assess the current state of sustainable development in China, this study employs the slacks-based super efficiency model (Super-SBM) to measure the the urban eco-efficiency in China (CUEE) of 284 cities. The study utilizes Kernel Density Estimation (KDE) and Spatial Autocorrelation Analysis (SAA) to investigate the fundamental patterns of CUEE in terms of inter-city differences and relationships. Complex Network Analysis (CNA) and Link Prediction methods are applied to examine the characteristics and future trends of the CUEE network. Additionally, Geodetector and Geographically Weighted Regression (GWR) are used to analyze the influencing factors of CUEE. The findings are as follows: Overall CUEE is relatively low but shows a steady increase. The spatial association network of CUEE is becoming more complex, with increasing association strengths. The Chengdu-Chongqing Economic Circle (CCEC) is expected to further enhance its spatial association strength and may emerge as a new core area. The effectiveness of the interactions among selected factors is greater than that of individual factors. Degree centrality (X1) is identified as a core explanatory factor influencing CUEE, showing a positive correlation with CUEE. Scientific expenditure (X5) is also positively correlated with CUEE. Local fiscal budget expenditure (X3), industrial output value of foreign-invested enterprises (X7), and total cargo transportation volume (X9) are negatively correlated with CUEE. The analytical framework and research conclusions of this study offer valuable insights into the development of urban ecological efficiency in China and provide constructive recommendations for promoting sustainable urban development.

A novel framework for evidence-based assessment of flood resilience integrating multi-source evidence: A case study of the Yangtze River Economic Belt, China

Floods are extremely destructive to the society, economy and nature, and severely restrict sustainable urban development. There is an urgent need to assess the level of flood resilience, analyze its evolutionary characteristics and improve the flood resilience of the region. However, few previous studies have integrated multi-source evidence into a framework for assessing flood resilience over a longer time span. This study integrated multi-source evidence to analyze the Yangtze River Economic Belt, including literature-based evidence, policy texts and social media data. Subsequently, the Kruskal algorithm and Jaccard coefficient were used to construct collinear networks and identify the clustering dimensions of flood resilience. After evidence judgment, a flood resilience indicator system was constructed. The flood resilience index was calculated using the improved Critic method. The dynamic evolution characteristics and key influencing factors were illustrated by the Kernel density and Grey correlation methods, respectively. The principal contribution is to integrate multi-source evidence to assess flood resilience, with a newly constructed indicator system that systematically considers local public demand, policy priorities and common indicators from previous literature. The results show that: the flood resilience index of the Yangtze River Economic Belt is in the range of [0.16, 0.75] from 2000 to 2022, with higher values in the downstream compared to those in the midstream and upstream. The social dimension dominating the overall flood resilience. The kernel density curve of the YREB is characterized by a right trailing. The inter-regional differences tend to widen and have a polarization effect. The special funds for water conservancy finances and the length of flood prevention levees are key factors influencing the level of flood resilience. Finally, strategies for enhancing flood resilience were proposed. This study provides a feasible framework for constructing an indicator system and assessing flood resilience by integrating multi-source data. It is important for flood risk management and helps to the development of urban flood prevention and resilience strategies.

Carbon Price Point–Interval Forecasting Based on Two-Layer Decomposition and Deep Learning Combined Model Using Weight Assignment

With the intensification of global warming, the demand for carbon emissions reduction has gradually increased in various countries. Carbon price is crucial for promoting the activation of the carbon trading market and facilitating emissions reduction. However, the current carbon price has non-linear characteristics, large fluctuations, and high complexity, making accurate predictions challenging. To effectively predict the trends and change of carbon price, this study proposed a hybrid deep learning point–interval prediction model. First, an improved variational mode decomposition–symplectic geometry mode decomposition (IVMD–SGMD) two-layer decomposition model was constructed to decompose the carbon prices into regular subsequences. Then, attention–temporal convolutional network–bidirectional gated recursive unit (Attention-TCN-BiGRU) and Encoder–Decoder long short-term memory (LSTM) combined prediction models were constructed for the prediction of subsequences. The entropy method (EM) was used to assign weights to the predictions of two models to achieve model complementarity and a linear reconstruction of the models’ results. Then the error correction was performed to obtain the final prediction results. This study conducted an experiment on carbon prices in the Guangdong and Shenzhen markets. The mean absolute error (MAE) of the two datasets were reduced by 89.69% and 87.43% lower than that for LSTM. To demonstrate the model's adaptability, prediction experiments conducted on natural gas and crude oil prices were employed, confirming its strong predictive accuracy in energy price forecasting. Based on the point prediction error, the interval prediction using the improved kernel density estimation (IKDE) provides more carbon market information for decision makers. The proposed model aids government energy policy formulation and fosters ongoing efforts to reduce carbon emissions.

Distribution reconstruction and reliability assessment of complex LSFs via an adaptive Non-parametric Density Estimation Method

Complex limit state functions (LSFs), often characterized by strong nonlinearity, non-smoothness, or discontinuity, pose challenges for structural reliability analysis in engineering practices. Conventional methods for uncertainty propagation and reliability assessment may struggle to handle these issues effectively. This paper introduces a novel approach to adaptively reconstruct the unknown distributions of complex LSFs. The Non-parametric Density Estimation Method based on Harmonic Transform (NDEM-HT) is employed as the tool for this purpose. An adaptive strategy is then proposed to determine the number of harmonic moments required in NDEM-HT for achieving high accuracy. Specifically, the Adaptive Kernel Density Estimation (AKDE) method is also adopted to provide an initial estimation of the rough distribution. Subsequently, the optimal number of harmonic moments is determined by minimizing the relative entropy between the distributions obtained by AKDE and NDEM-HT. The efficacy of the proposed method is demonstrated through five numerical examples, considering various types of complex LSFs. Comparative results are also provided employing MCS along with both conventional and state-of-the-art methods.

A meta-analysis of cognitive flexibility in aging: Perspective from functional network and lateralization.

Cognitive flexibility, the ability to switch between mental processes to generate appropriate behavioral responses, is reduced with typical aging. Previous studies have found that age-related declines in cognitive flexibility are often accompanied by variations in the activation of multiple regions. However, no meta-analyses have examined the relationship between cognitive flexibility in aging and age-related variations in activation within large-scale networks. Here, we conducted a meta-analysis employing multilevel kernel density analysis to identify regions with different activity patterns between age groups, and determined how these regions fall into functional networks. We also employed lateralization analysis to explore the spatial distribution of regions exhibiting group differences in activation. The permutation tests based on Monte Carlo simulation were used to determine the significance of the activation and lateralization results. The results showed that cognitive flexibility in aging was associated with both decreased and increased activation in several functional networks. Compared to young adults, older adults exhibited increased activation in the default mode, dorsal attention, ventral attention, and somatomotor networks, while displayed decreased activation in the visual network. Moreover, we found a global-level left lateralization for regions with decreased activation, but no lateralization for regions with higher activation in older adults. At the network level, the regions with decreased activation were left-lateralized, while the regions with increased activation showed varying lateralization patterns within different networks. To sum up, we found that networks that support various mental functions contribute to age-related variations in cognitive flexibility. Additionally, the aging brain exhibited network-dependent activation and lateralization patterns in response to tasks involving cognitive flexibility. We highlighted that the comprehensive meta-analysis in this study offered new insights into understanding cognitive flexibility in aging from a network perspective.

Joint probabilistic modeling approach for harmonic and three-phase unbalanced disturbance sources

Harmonics and three-phase imbalance are two common disturbances in power systems that interact with and affect each other, leading to more complex impacts on power system performance. To comprehensively and accurately analyze the distribution and interaction mechanisms of harmonics and three-phase imbalance, this study investigated the joint emission level of harmonic and three-phase unbalanced disturbance sources (H-TU-DS). This paper proposes a joint probabilistic emission level modeling approach. The power, harmonic, and three-phase unbalanced data of H-TU-DS are multidimensional, and the feature dataset is filtered by calculating multiple correlation coefficients to achieve dimensionality reduction without losing data information. Considering the different operating characteristics of the H-TU-DS, an improved fuzzy C-means (FCM) algorithm is applied to classify operating conditions, enabling a comprehensive and accurate analysis of the joint emission level. Based on the nonparametric kernel density function, joint probability modeling of H-TU-DS is performed using an adaptive bandwidth improvement method, effectively enhancing the accuracy of the modeling process. Finally, the effectiveness and accuracy of the proposed methods for feature dataset filtering, operating condition classification, and joint probability modeling are demonstrated through comparisons with both simulated and actual data. The proposed model facilitates the prediction and assessment of the impact of H-TU-DS on power quality after grid connection, enabling the effective prevention of power-quality problems through advanced treatment.